Possible remainders of a square
Number Theory
Level
5
Let \[N= 3 \times 5 \times 7 \times 11 \times 13\] There are \(X\) possibilities for the units digit of a perfect square when it is represented in base \(N\). Compute the last three digits of \(X\) (in base 10).
Details and assumptions
We are talking about \(3, 5, 7, 11, 13\) in their decimal representations.
You might use the fact that \(3, 5, 7, 11, 13\) are all primes.
by
Sreejato Bhattacharya