Problems & Puzzles: Puzzles

Puzzle 393. A follow up to Puzzle 128

In Puzzle 128 we asked for sums of consecutive and squared primes equal to another squared prime. Almost three years ago Giovanni Resta found only one solution:

2489647^2 = 355363^2 + (other 47 terms) + 355951^2

Q.1. Find a sum of consecutive cubed primes equal to another cube (prime or not)

A related challenge comes from Kevin Brown's statement

"it appears that there are no sums of two or more consecutive 4th powers equal to a 4th power, or in general sums of two or more consecutive nth powers equal to an nth power for any n>3"

Q.2 Find a counterexample to the Brown's statement



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