For a positive integer x, we define the function Y, as follows:
; and
for 
.Hence, for 
we have:
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.
, 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.
, that satisfies the above congruence.For 
, 
and 
, we see that only and 
satisfies the congruence, since:
, 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, 
.
, and , the above equation is satisfied, .Therefore: S(20,10,3) = sum(1:20) = 210.
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I am getting all test solutions correct except: test2, test5, and test8.
For test2 for example, I am only getting [1 5] = 6.
Hi David, test suites has been corrected. Please try again. Thanks.