n
Anzahl der Lösungen (Folge A076427 in OEIS )
Zahlen
k
{\displaystyle k}
k
+
n
{\displaystyle k+n}
k
{\displaystyle k}
A103953 in OEIS )
x
p
−
y
q
=
n
{\displaystyle x^{p}-y^{q}=n}
1
1
8
3
2
−
2
3
=
1
{\displaystyle 3^{2}-2^{3}=1}
2
1
25
3
3
−
5
2
=
2
{\displaystyle 3^{3}-5^{2}=2}
3
2
1, 125
2
2
−
1
q
=
3
{\displaystyle 2^{2}-1^{q}=3}
2
7
−
5
3
=
3
{\displaystyle 2^{7}-5^{3}=3}
4
3
4, 32, 121
2
3
−
2
2
=
4
{\displaystyle 2^{3}-2^{2}=4}
6
2
−
2
5
=
4
{\displaystyle 6^{2}-2^{5}=4}
5
3
−
11
2
=
4
{\displaystyle 5^{3}-11^{2}=4}
5
2
4, 27
3
2
−
2
2
=
5
{\displaystyle 3^{2}-2^{2}=5}
2
5
−
3
3
=
5
{\displaystyle 2^{5}-3^{3}=5}
6
0
es existiert keine Lösung
7
5
1, 9, 25, 121, 32761
2
3
−
1
q
=
7
{\displaystyle 2^{3}-1^{q}=7}
4
2
−
3
2
=
7
{\displaystyle 4^{2}-3^{2}=7}
2
5
−
5
2
=
7
{\displaystyle 2^{5}-5^{2}=7}
2
7
−
11
2
=
7
{\displaystyle 2^{7}-11^{2}=7}
32
3
−
181
2
=
7
{\displaystyle 32^{3}-181^{2}=7}
8
3
1, 8, 97336
3
2
−
1
q
=
8
{\displaystyle 3^{2}-1^{q}=8}
2
4
−
2
3
=
8
{\displaystyle 2^{4}-2^{3}=8}
312
2
−
46
3
=
8
{\displaystyle 312^{2}-46^{3}=8}
9
4
16, 27, 216, 64000
5
2
−
2
4
=
9
{\displaystyle 5^{2}-2^{4}=9}
6
2
−
3
3
=
9
{\displaystyle 6^{2}-3^{3}=9}
15
2
−
6
3
=
9
{\displaystyle 15^{2}-6^{3}=9}
253
2
−
40
3
=
9
{\displaystyle 253^{2}-40^{3}=9}
10
1
2187
13
3
−
3
7
=
10
{\displaystyle 13^{3}-3^{7}=10}
11
4
16, 25, 3125, 3364
3
3
−
2
4
=
11
{\displaystyle 3^{3}-2^{4}=11}
6
2
−
5
2
=
11
{\displaystyle 6^{2}-5^{2}=11}
56
2
−
5
5
=
11
{\displaystyle 56^{2}-5^{5}=11}
15
3
−
58
2
=
11
{\displaystyle 15^{3}-58^{2}=11}
12
2
4, 2197
2
4
−
2
2
=
12
{\displaystyle 2^{4}-2^{2}=12}
47
2
−
13
3
=
12
{\displaystyle 47^{2}-13^{3}=12}
13
3
36, 243, 4900
7
2
−
6
2
=
13
{\displaystyle 7^{2}-6^{2}=13}
2
8
−
3
5
=
13
{\displaystyle 2^{8}-3^{5}=13}
17
3
−
70
2
=
13
{\displaystyle 17^{3}-70^{2}=13}
14
0
es existiert keine Lösung
15
3
1, 49, 1295029
2
4
−
1
q
=
15
{\displaystyle 2^{4}-1^{q}=15}
2
6
−
7
2
=
15
{\displaystyle 2^{6}-7^{2}=15}
1138
2
−
109
3
=
15
{\displaystyle 1138^{2}-109^{3}=15}
16
3
9, 16, 128
5
2
−
3
2
=
16
{\displaystyle 5^{2}-3^{2}=16}
2
5
−
2
4
=
16
{\displaystyle 2^{5}-2^{4}=16}
12
2
−
2
7
=
16
{\displaystyle 12^{2}-2^{7}=16}
17
7
8, 32, 64, 512, 79507, 140608, 143384152904
5
2
−
2
3
=
17
{\displaystyle 5^{2}-2^{3}=17}
7
2
−
2
5
=
17
{\displaystyle 7^{2}-2^{5}=17}
3
4
−
2
6
=
17
{\displaystyle 3^{4}-2^{6}=17}
23
2
−
2
9
=
17
{\displaystyle 23^{2}-2^{9}=17}
282
2
−
43
3
=
17
{\displaystyle 282^{2}-43^{3}=17}
375
2
−
52
3
=
17
{\displaystyle 375^{2}-52^{3}=17}
378661
2
−
5234
3
=
17
{\displaystyle 378661^{2}-5234^{3}=17}
18
3
9, 225, 343
3
3
−
3
2
=
18
{\displaystyle 3^{3}-3^{2}=18}
3
5
−
15
2
=
18
{\displaystyle 3^{5}-15^{2}=18}
19
2
−
7
3
=
18
{\displaystyle 19^{2}-7^{3}=18}
19
5
8, 81, 125, 324, 503284356
3
3
−
2
3
=
19
{\displaystyle 3^{3}-2^{3}=19}
10
2
−
3
4
=
19
{\displaystyle 10^{2}-3^{4}=19}
12
2
−
5
3
=
19
{\displaystyle 12^{2}-5^{3}=19}
7
3
−
18
2
=
19
{\displaystyle 7^{3}-18^{2}=19}
55
5
−
22434
2
=
19
{\displaystyle 55^{5}-22434^{2}=19}
20
2
16, 196
6
2
−
2
4
=
20
{\displaystyle 6^{2}-2^{4}=20}
6
3
−
14
2
=
20
{\displaystyle 6^{3}-14^{2}=20}
21
2
4, 100
5
2
−
2
2
=
21
{\displaystyle 5^{2}-2^{2}=21}
11
2
−
10
2
=
21
{\displaystyle 11^{2}-10^{2}=21}
22
2
27, 2187
7
2
−
3
3
=
22
{\displaystyle 7^{2}-3^{3}=22}
47
2
−
3
7
=
22
{\displaystyle 47^{2}-3^{7}=22}
23
4
4, 9, 121, 2025
3
3
−
2
2
=
23
{\displaystyle 3^{3}-2^{2}=23}
2
5
−
3
2
=
23
{\displaystyle 2^{5}-3^{2}=23}
12
2
−
11
2
=
23
{\displaystyle 12^{2}-11^{2}=23}
2
11
−
45
2
=
23
{\displaystyle 2^{11}-45^{2}=23}
24
5
1, 8, 25, 1000, 542939080312
5
2
−
1
q
=
24
{\displaystyle 5^{2}-1^{q}=24}
2
5
−
2
3
=
24
{\displaystyle 2^{5}-2^{3}=24}
7
2
−
5
2
=
24
{\displaystyle 7^{2}-5^{2}=24}
2
10
−
10
3
=
24
{\displaystyle 2^{10}-10^{3}=24}
736844
2
−
8158
3
=
24
{\displaystyle 736844^{2}-8158^{3}=24}
25
2
100, 144
5
3
−
10
2
=
25
{\displaystyle 5^{3}-10^{2}=25}
13
2
−
12
2
=
25
{\displaystyle 13^{2}-12^{2}=25}
26
3
1, 42849, 6436343
3
3
−
1
q
=
26
{\displaystyle 3^{3}-1^{q}=26}
35
3
−
207
2
=
26
{\displaystyle 35^{3}-207^{2}=26}
2537
2
−
23
5
=
26
{\displaystyle 2537^{2}-23^{5}=26}
27
3
9, 169, 216
6
2
−
3
2
=
27
{\displaystyle 6^{2}-3^{2}=27}
14
2
−
13
2
=
27
{\displaystyle 14^{2}-13^{2}=27}
3
5
−
6
3
=
27
{\displaystyle 3^{5}-6^{3}=27}
28
7
4, 8, 36, 100, 484, 50625, 131044
2
5
−
2
2
=
28
{\displaystyle 2^{5}-2^{2}=28}
6
2
−
2
3
=
28
{\displaystyle 6^{2}-2^{3}=28}
2
6
−
6
2
=
28
{\displaystyle 2^{6}-6^{2}=28}
2
7
−
10
2
=
28
{\displaystyle 2^{7}-10^{2}=28}
2
9
−
22
2
=
28
{\displaystyle 2^{9}-22^{2}=28}
37
3
−
225
2
=
28
{\displaystyle 37^{3}-225^{2}=28}
2
17
−
362
2
=
28
{\displaystyle 2^{17}-362^{2}=28}
29
1
196
15
2
−
14
2
=
29
{\displaystyle 15^{2}-14^{2}=29}
30
1
6859
83
2
−
19
3
=
30
{\displaystyle 83^{2}-19^{3}=30}
31
2
1, 225
2
5
−
1
q
=
31
{\displaystyle 2^{5}-1^{q}=31}
16
2
−
15
2
=
31
{\displaystyle 16^{2}-15^{2}=31}
32
4
4, 32, 49, 7744
6
2
−
2
2
=
32
{\displaystyle 6^{2}-2^{2}=32}
2
6
−
2
5
=
32
{\displaystyle 2^{6}-2^{5}=32}
3
4
−
7
2
=
32
{\displaystyle 3^{4}-7^{2}=32}
6
5
−
88
2
=
32
{\displaystyle 6^{5}-88^{2}=32}
n
Anzahl der Lösungen (Folge A076427 in OEIS )
Zahlen
k
{\displaystyle k}
k
+
n
{\displaystyle k+n}
k
{\displaystyle k}
A103953 in OEIS )
x
p
−
y
q
=
n
{\displaystyle x^{p}-y^{q}=n}
33
2
16, 256
7
2
−
2
4
=
33
{\displaystyle 7^{2}-2^{4}=33}
17
2
−
2
8
=
33
{\displaystyle 17^{2}-2^{8}=33}
34
0
es existiert keine Lösung
35
3
1, 289, 1296
6
2
−
1
q
=
35
{\displaystyle 6^{2}-1^{q}=35}
18
2
−
17
2
=
35
{\displaystyle 18^{2}-17^{2}=35}
11
3
−
36
2
=
35
{\displaystyle 11^{3}-36^{2}=35}
36
2
64, 1728
10
2
−
2
6
=
36
{\displaystyle 10^{2}-2^{6}=36}
42
2
−
12
3
=
36
{\displaystyle 42^{2}-12^{3}=36}
37
3
27, 324, 14348907
2
6
−
3
3
=
37
{\displaystyle 2^{6}-3^{3}=37}
19
2
−
18
2
=
37
{\displaystyle 19^{2}-18^{2}=37}
3788
2
−
243
3
=
37
{\displaystyle 3788^{2}-243^{3}=37}
38
1
1331
37
2
−
11
3
=
38
{\displaystyle 37^{2}-11^{3}=38}
39
4
25, 361, 961, 10609
2
6
−
5
2
=
39
{\displaystyle 2^{6}-5^{2}=39}
20
2
−
19
2
=
39
{\displaystyle 20^{2}-19^{2}=39}
10
3
−
31
2
=
39
{\displaystyle 10^{3}-31^{2}=39}
22
3
−
103
2
=
39
{\displaystyle 22^{3}-103^{2}=39}
40
4
9, 81, 216, 2704
7
2
−
3
2
=
40
{\displaystyle 7^{2}-3^{2}=40}
11
2
−
3
4
=
40
{\displaystyle 11^{2}-3^{4}=40}
2
8
−
6
3
=
40
{\displaystyle 2^{8}-6^{3}=40}
14
3
−
52
2
=
40
{\displaystyle 14^{3}-52^{2}=40}
41
3
8, 128, 400
7
2
−
2
3
=
41
{\displaystyle 7^{2}-2^{3}=41}
13
2
−
2
7
=
41
{\displaystyle 13^{2}-2^{7}=41}
21
2
−
20
2
=
41
{\displaystyle 21^{2}-20^{2}=41}
42
0
es existiert keine Lösung
43
1
441
22
2
−
21
2
=
43
{\displaystyle 22^{2}-21^{2}=43}
44
3
81, 100, 125
5
3
−
3
4
=
44
{\displaystyle 5^{3}-3^{4}=44}
12
2
−
10
2
=
44
{\displaystyle 12^{2}-10^{2}=44}
13
2
−
5
3
=
44
{\displaystyle 13^{2}-5^{3}=44}
45
4
4, 36, 484, 9216
7
2
−
2
2
=
45
{\displaystyle 7^{2}-2^{2}=45}
9
2
−
6
2
=
45
{\displaystyle 9^{2}-6^{2}=45}
23
2
−
22
2
=
45
{\displaystyle 23^{2}-22^{2}=45}
21
3
−
96
2
=
45
{\displaystyle 21^{3}-96^{2}=45}
46
1
243
17
2
−
3
5
=
46
{\displaystyle 17^{2}-3^{5}=46}
47
6
81, 169, 196, 529, 1681, 250000
2
7
−
3
4
=
47
{\displaystyle 2^{7}-3^{4}=47}
6
3
−
13
2
=
47
{\displaystyle 6^{3}-13^{2}=47}
3
5
−
14
2
=
47
{\displaystyle 3^{5}-14^{2}=47}
24
2
−
23
2
=
47
{\displaystyle 24^{2}-23^{2}=47}
12
3
−
41
2
=
47
{\displaystyle 12^{3}-41^{2}=47}
63
3
−
500
2
=
47
{\displaystyle 63^{3}-500^{2}=47}
48
4
1, 16, 121, 21904
7
2
−
2
0
=
48
{\displaystyle 7^{2}-2^{0}=48}
2
6
−
2
4
=
48
{\displaystyle 2^{6}-2^{4}=48}
13
2
−
11
2
=
48
{\displaystyle 13^{2}-11^{2}=48}
28
3
−
148
2
=
48
{\displaystyle 28^{3}-148^{2}=48}
49
3
32, 576, 274576
3
4
−
2
5
=
49
{\displaystyle 3^{4}-2^{5}=49}
25
2
−
24
2
=
49
{\displaystyle 25^{2}-24^{2}=49}
65
3
−
524
2
=
49
{\displaystyle 65^{3}-524^{2}=49}
50
0
es existiert keine Lösung
51
2
49, 625
10
2
−
7
2
=
51
{\displaystyle 10^{2}-7^{2}=51}
26
2
−
5
4
=
51
{\displaystyle 26^{2}-5^{4}=51}
52
1
144
14
2
−
12
2
=
52
{\displaystyle 14^{2}-12^{2}=52}
53
2
676, 24336
27
2
−
26
2
=
53
{\displaystyle 27^{2}-26^{2}=53}
29
3
−
156
2
=
53
{\displaystyle 29^{3}-156^{2}=53}
54
2
27, 289
3
4
−
3
3
=
54
{\displaystyle 3^{4}-3^{3}=54}
7
3
−
17
2
=
54
{\displaystyle 7^{3}-17^{2}=54}
55
3
9, 729, 175561
2
6
−
3
2
=
55
{\displaystyle 2^{6}-3^{2}=55}
28
2
−
27
2
=
55
{\displaystyle 28^{2}-27^{2}=55}
56
3
−
419
2
=
55
{\displaystyle 56^{3}-419^{2}=55}
56
4
8, 25, 169, 5776
2
6
−
2
3
=
56
{\displaystyle 2^{6}-2^{3}=56}
3
4
−
5
2
=
56
{\displaystyle 3^{4}-5^{2}=56}
15
2
−
13
2
=
56
{\displaystyle 15^{2}-13^{2}=56}
18
3
−
76
2
=
56
{\displaystyle 18^{3}-76^{2}=56}
57
3
64, 343, 784
11
2
−
2
6
=
57
{\displaystyle 11^{2}-2^{6}=57}
20
2
−
7
3
=
57
{\displaystyle 20^{2}-7^{3}=57}
29
2
−
28
2
=
57
{\displaystyle 29^{2}-28^{2}=57}
58
0
es existiert keine Lösung
59
1
841
30
2
−
29
2
=
59
{\displaystyle 30^{2}-29^{2}=59}
60
4
4, 196, 2515396, 2535525316
2
6
−
2
2
=
60
{\displaystyle 2^{6}-2^{2}=60}
2
8
−
14
2
=
60
{\displaystyle 2^{8}-14^{2}=60}
136
3
−
1586
2
=
60
{\displaystyle 136^{3}-1586^{2}=60}
76
5
−
50354
2
=
60
{\displaystyle 76^{5}-50354^{2}=60}
61
2
64, 900
5
3
−
2
6
=
61
{\displaystyle 5^{3}-2^{6}=61}
31
2
−
30
2
=
61
{\displaystyle 31^{2}-30^{2}=61}
62
0
es existiert keine Lösung
63
4
1, 81, 961, 183250369
2
6
−
1
q
=
63
{\displaystyle 2^{6}-1^{q}=63}
12
2
−
9
2
=
63
{\displaystyle 12^{2}-9^{2}=63}
2
10
−
31
2
=
63
{\displaystyle 2^{10}-31^{2}=63}
568
3
−
13537
2
=
63
{\displaystyle 568^{3}-13537^{2}=63}
64
4
36, 64, 225, 512
10
2
−
6
2
=
64
{\displaystyle 10^{2}-6^{2}=64}
2
7
−
2
6
=
64
{\displaystyle 2^{7}-2^{6}=64}
17
2
−
15
2
=
64
{\displaystyle 17^{2}-15^{2}=64}
24
2
−
2
9
=
64
{\displaystyle 24^{2}-2^{9}=64}
65
4
16, 1024, 2744, 199176704
3
4
−
2
4
=
65
{\displaystyle 3^{4}-2^{4}=65}
33
2
−
2
10
=
65
{\displaystyle 33^{2}-2^{10}=65}
53
2
−
14
3
=
65
{\displaystyle 53^{2}-14^{3}=65}
14113
2
−
584
3
=
65
{\displaystyle 14113^{2}-584^{3}=65}
66
0
es existiert keine Lösung
67
2
1089, 12100
34
2
−
33
2
=
67
{\displaystyle 34^{2}-33^{2}=67}
23
3
−
110
2
=
67
{\displaystyle 23^{3}-110^{2}=67}
...
100
10
25, 125, 243, 576, 900, 3025, 8000, 13824, 39204, 18821096000
5
3
−
5
2
=
100
{\displaystyle 5^{3}-5^{2}=100}
15
2
−
5
3
=
100
{\displaystyle 15^{2}-5^{3}=100}
7
3
−
3
5
=
100
{\displaystyle 7^{3}-3^{5}=100}
26
2
−
24
2
=
100
{\displaystyle 26^{2}-24^{2}=100}
10
3
−
30
2
=
100
{\displaystyle 10^{3}-30^{2}=100}
5
5
−
55
2
=
100
{\displaystyle 5^{5}-55^{2}=100}
90
2
−
20
3
=
100
{\displaystyle 90^{2}-20^{3}=100}
118
2
−
24
3
=
100
{\displaystyle 118^{2}-24^{3}=100}
34
3
−
198
2
=
100
{\displaystyle 34^{3}-198^{2}=100}
137190
2
−
2660
3
=
100
{\displaystyle 137190^{2}-2660^{3}=100}
