Modulo makes it weak

Number Theory Level 3

Consider a smallest positive integer PP which is divisible by all natural numbers from 11 to 100100 inclusive. If bb is a non-negative integer, PP satisfy the congruence P≡b(mod9699690)P \equiv b \pmod {9699690} Find the smallest value of bb.

Details and Assumptions

  • You may need to refer to list of primes as a reference.

  • No computational aid is required in solving this problem.

Nihar Mahajan by Nihar Mahajan
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