As a small illustration of Chinese remainder theorem that can all be solved mentally, say M = 30. Let’s say we express this M as the product of the pair wise co primes 2, 3, and 5. That is, m1 = 2, m2 = 3, and m3 = 5. Given that the numbers involved are small, calculate (75 + 89) mod 30,  (75 × 89) mod 30, etc., using the Chinese Remainder Theorem. Verify your answers by  direct computations on the operands in each case.

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A: This problem can be solve by using congruences. So I can do it in Advanced mathematics.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.