Modulo makes it weak
Number Theory
Level
3
Consider a smallest positive integer \(P\) which is divisible by all natural numbers from \(1\) to \(100\) inclusive. If \(b\) is a non-negative integer, \(P\) satisfy the congruence \[P \equiv b \pmod {9699690} \] Find the smallest value of \(b\).
Details and Assumptions
You may need to refer to list of primes as a reference.
No computational aid is required in solving this problem.
by
Nihar Mahajan