Problem 55595. Easy Sequences 87: Perfect Power Modular Residue of a Nested Sum-product Function

For a positive integer x, we define the function Y, as follows:
; and
for .
Hence, for we have:
And if :
We now consider the following congruence:
with Mand
The congruence expresses the possibility that the nested sum and product function defined above (Y), can have a perfect power residue in some modular base. In fact, solving for x, the congruence always have a trivial solution, namely , that's because , which is, of course, a perfect power in any modular base.
Given the value of integers N, M, and certain limit L, find the sum S of all positive integer values of , that satisfies the above congruence.
For , and , we see that only and satisfies the congruence, since:
; and
Therefore in this case S(20,7,3) = 1 + 5 = 6.
For , and , the above equation is satisfied, .
Therefore: S(20,10,3) = sum(1:20) = 210.

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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Jan 02, 2023

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