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:
Hence, for
we have:
And if
:
-----------------------------
We now consider the following congruence:
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:
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.
Solution Stats
Problem Comments
-
2 Comments
David Hill
on 1 Jan 2023
I am getting all test solutions correct except: test2, test5, and test8.
For test2 for example, I am only getting [1 5] = 6.
Ramon Villamangca
on 2 Jan 2023
Hi David, test suites has been corrected. Please try again. Thanks.
Solution Comments
Show commentsProblem Recent Solvers2
Suggested Problems
-
22223 Solvers
-
570 Solvers
-
Create a square matrix of multiples
469 Solvers
-
Determine the number of odd integers in a vector
709 Solvers
-
Sum the numbers on the main diagonal
576 Solvers
More from this Author116
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!