Non-coinciding Primes
A prime is said to be non-coinciding if there exists a positive integer such that no two powers of have their rightmost digits the same, in the same order.
Determine the sum of all non-coinciding primes .
The answer is 0.
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1 solution
There are no such primes, by the Pigeonhole Principle. For any k there are finitely many possibilities for the k rightmost digits, and there are infinitely many powers of p , so there must be a pair whose k rightmost digits coincide.