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 A^2 = B^3 + C^3
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 smallest integer whose first n multiples all contain a 3
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 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Tag Archives: 4th Powers
Sums of consecutive integers that result in a 4th 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
ndigit numbers whose 4th powers end with the same n digits
…………………………………………………………… …………………………………………………………… ……………………………………………………….. ……………………………………………………….. … Continue reading
x^4 + y^4 = z^2 ± 1
Here are the solutions for all Find solutions for,
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
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:
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
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
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
Posted in Number Puzzles
Tagged 4th Powers, 5th Powers, Sums of 4th Powers, Sums of 5th powers
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Powers of Num3ers and their digits
A review of older posts Num3er N and N^2 use all digits 09 once Both 854 and 854^2 use all digits 1 to 9 854 854^2 = … Continue reading