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.


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