Find the smallest number which leaves 22, 35, 48 and 61 as remainders when divided by 26, 39, 52 and 65 respectively.760776766780None of these
Question
Solution 1
The problem is asking for the smallest number that satisfies a system of linear congruences. This is a classic problem in number theory and can be solved using the Chinese Remainder Theorem (CRT).
The system of congruences is:
x ≡ 22 (mod 26) x ≡ 35 (mod 39) x ≡ 48 (mod 52) x ≡ 61 (mod 65)
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