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91 =

91 =. 91 = 8 2 + 3 3. 91 =. 91 = 8 2 + 3 3. 91 = 3 3 + 4 3. 91 =. 91 = 8 2 + 3 3. 91 = 3 3 + 4 3. 91 = 3 3 + 2 6. 91 = 8 2 + 3 3. 91 = 3 3 + 4 3. 91 = 3 3 + 2 6. 91 = 8 2 + 3 3. 91 = 3 3 + 4 3. 91 = 3 3 + 2 6. 91 = 8 2 + 3 3. 91 = 3 3 + 2 6. 92 =. 91 = 8 2 + 3 3.

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91 =

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  1. 91 =

  2. 91 = 82 + 33 91 =

  3. 91 = 82 + 33 91 = 33 + 43 91 =

  4. 91 = 82 + 33 91 = 33 + 43 91 = 33 + 26

  5. 91 = 82 + 33 91 = 33 + 43 91 = 33 + 26

  6. 91 = 82 + 33 91 = 33 + 43 91 = 33 + 26

  7. 91 = 82 + 33 91 = 33 + 26

  8. 92 = 91 = 82 + 33 91 = 33 + 26

  9. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 =

  10. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 82 + 33 + 14 92 =

  11. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 82 + 33 + 14 92 = 33 + 26 + 14

  12. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 82 + 33 + 19 92 = 33 + 26 + 19

  13. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 82 + 33 + 110 92 = 33 + 26 + 110

  14. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 82 + 33 + 110 92 = 33 + 26 + 110

  15. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 82 + 33 + 110 92 = 33 + 26 + 110

  16. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26

  17. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 92 + 111

  18. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 92 + 111

  19. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26 92 = 92 + 111

  20. 92 = 72 + 33 + 24 91 = 82 + 33 91 = 33 + 26

  21. 292 = • Rules: • 1) All of the exponents must be different. • 91 = 33 + 43 • 2) All of the bases must be greater than one. • 92 = 33 + 26 + 14 • 3) All of the exponents must be greater than one. • 92 = 92 + 111

  22. 292 = 142 + 43 + 25 292 = 142 + 25 + 26 292 = 132 + 33 + 25 + 26 292 = 112 + 33 + 24 + 27 292 = 102 + 43 + 27 292 = 102 + 26 + 27 292 = 72 + 35 292 = 62 + 43 + 26 + 27 292 = 62 + 44 292 = 62 + 28 292 = 52 + 33 + 24 + 25 + 26 + 27 292 = 52 + 23 + 24 + 35 292 = 32 + 33 + 44 292 = 32 + 33 + 28 292 = 22 + 43 + 25 + 26 + 27 292 = 22 + 44 + 25 292 = 22 + 25 + 28

  23. 291 = • Rules: • 1) All of the exponents must be different. • 91 = 33 + 43 • 2) All of the bases must be greater than one. • 92 = 33 + 26 + 14 • 3) All of the exponents must be greater than one. • 92 = 92 + 111

  24. Polignac’s 2n + p conjecture 3 = 20 + 2 5 = 21 + 3 7 = 22 + 3 or 21 + 5 9 = 22 + 5 or 21 + 7 11 = 23 + 3 or 22 + 7 13 = 23 + 5 or 21 + 11 15 = 23 + 7 or 22 + 11 17 = 22 + 13 19 = 24 + 3 or 23 + 11 or 21 + 17 21 = 24 + 5 or 23 + 13 or 22 + 17 or 21 + 19

  25. 127, 149, 251, 331, 337, 373, 509, 599, 701, 757, 809, 877, 905, 907, 959, 977, 997, 1019, 1087, 1199, 1207, 1211, 1243, 1259, 1271, 1477, 1529, 1541, 1549, 1589, 1597, 1619, 1649, 1657, 1719, 1759, 1777, 1783, 1807, 1829, 1859, 1867, 1927, 1969, 1973

  26. Armstrong Numbers 153 = 13 + 53 + 33 370 = 33 + 73 + 03 371 = 33 + 73 + 13 407 = 43 + 03 + 73 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 54,748 = 55 + 45 + 75 + 45 + 85 92,727 = 95 + 25 + 75 + 25 + 75 93,084 = 95 + 35 + 05 + 85 + 45

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