Tag Archives: 4-th Powers

Sums of consecutive integers that result in a 4-th power

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 … Continue reading

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n-digit numbers whose 4th powers end with the same n digits

                                                                                                                                      …………………………………………………………… ……………………………………………………………                                                                                                           ……………………………………………………….. ………………………………………………………..               … Continue reading

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x^4 + y^4 = z^2 ± 1

      Here are the solutions for all       Find solutions for,                                    

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Primitive Pythagorean triples(a,b,c); (a*b)^4 + (a*c)^4 + (b*c)^4

    A Pythagorean triple consists of three positive integers   a,   b,   and c,   such that                             and the sum is a square:   ……………………..   (1) OR the sum is a product of two … Continue reading

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Num3ers whose 4th power are the sum of two cubes: N^4 = A^3 + B^3

      Extend the list to   N ≤ 1000     Paul’s solutions:                                          

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Puzzle| N^4 = A^4 + B^4 – C^4

               

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Prime numbers such that the sum of the digits raised to the 4th power is also a prime

The prime numbers under 1000 : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, … Continue reading

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A^4 + B^4 + C^4 + D^4 = E^4

  Mathematician Noam D. Elkies found: 2682440^4   +   15365639^4   +   18796760^4   =   20615673^4                                                    ——————————————        30^4   +   120^4   +   315^4   +   272^4   =   … Continue reading

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a^k + 2b^k + 2c^k = d^k, where k = 4, 5

                                       (1)   a^4   +   2 b^4   +   2 c^4   =   d^4                                      (2)   a^5   +   2 b^5   +   2 c^5   =   d^5   (1) 2^4 … Continue reading

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Powers of Num3ers and their digits

                                                   A review of older posts       Num3er N and N^2 use all digits 0-9 once Both   854   and   854^2   use all digits   1   to   9 854 854^2   =   … Continue reading

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