Le soluzioni intere dell’equazione x5 + y5 = cz5, con 0 < x ≤ 5000, –5000 ≤ y < 0, per 0 < c ≤ 109, non multiplo di quinte potenze e non uguale a una somma di quinte potenze

La tabella seguente riporta le soluzioni intere dell’equazione x5 + y5 = cz5, con 0 < x ≤ 5000, –5000 ≤ y < 0, per 0 < c ≤ 109, non multiplo di quinte potenze e non uguale a una differenza di quinte potenze.

c

x

y

z

1222981

33

–1

2

1641301

35

–3

2

2166901

37

–5

2

2818981

39

–7

2

3618661

41

–9

2

4588981

43

–11

2

5754901

45

–13

2

7143301

47

–15

2

8782981

49

–17

2

9933275

276

–71

11

10704661

51

–19

2

12940981

53

–21

2

15526501

55

–23

2

18497701

57

–25

2

21892981

59

–27

2

25752661

61

–29

2

30118981

63

–31

2

35036101

65

–33

2

36259082

65

–1

2

40550101

67

–35

2

42191402

67

–3

2

46708981

69

–37

2

48126044

791

–787

11

48875882

69

–5

2

53562661

71

–39

2

56381642

71

–7

2

61162981

73

–41

2

64781642

73

–9

2

69563701

75

–43

2

74152682

75

–11

2

78820501

77

–45

2

82057551

421

–100

11

84575402

77

–13

2

88990981

79

–47

2

90153277

431

–204

11

96134282

79

–15

2

100134661

81

–49

2

108917642

81

–17

2

112312981

83

–51

2

123017642

83

–19

2

125589301

85

–53

2

138530282

85

–21

2

140028901

87

–55

2

155555402

87

–23

2

155698981

89

–57

2

172668661

91

–59

2

174196682

89

–25

2

191008981

93

–61

2

194561642

91

–27

2

210792901

95

–63

2

216761642

93

–29

2

232095301

97

–65

2

240911882

95

–31

2

254992981

99

–67

2

267131402

97

–33

2

268354383

97

–1

2

279564661

101

–69

2

295543082

99

–35

2

305890981

103

–71

2

326273642

101

–37

2

328440543

101

–5

2

330031274

625

–531

11

334054501

105

–73

2

359453642

103

–39

2

362272623

103

–7

2

364139701

107

–75

2

395217482

105

–41

2

396232981

109

–77

2

430422661

111

–79

2

433703402

107

–43

2

438292383

107

–11

2

466798981

113

–81

2

475053482

109

–45

2

480808383

109

–13

2

505454101

115

–83

2

519413642

111

–47

2

546482101

117

–85

2

566933642

113

–49

2

575716623

113

–17

2

589978981

119

–87

2

617767082

115

–51

2

628471743

115

–19

2

636042661

121

–89

2

672071402

117

–53

2

684772981

123

–91

2

688320626

645

–239

11

730007882

119

–55

2

736271701

125

–93

2

745534383

119

–23

2

790642501

127

–95

2

791741642

121

–57

2

810239343

121

–25

2

847990981

129

–97

2

857441642

123

–59

2

908424661

131

–99

2

927280682

125

–61

2

943484151

716

–515

11

953033343

125

–29

2

972052981

133

–101

2