What is the smallest positive integer satisfying the system of congruences: , , and ?
Answer and explanation
Correct answer: D.
- Step 1: Apply Chinese Remainder Theorem: moduli are pairwise coprime, with .
- Step 2: Combine and : since remainder is 2 for both, .
- Step 3: Express and substitute into third condition: .
- Step 4: Smallest non-negative .
Answer
23.
Why not the others: '' gives ; '' gives but ; '' is another residue.
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