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Home » Ready to Rock Your Party? These Must-Have Tips Are Perfection! - Network4

Ready to Rock Your Party? These Must-Have Tips Are Perfection! - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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Solution: Let $ x $ be the two-digit number. We are given:
x \equiv 1 \pmod{7}, \quad x \equiv 3 \pmod{5}
We solve this system using the Chinese Remainder Theorem.
Let $ x = 7k + 1 $. Substitute into the second congruence:
7k + 1 \equiv 3 \pmod{5} \Rightarrow 7k \equiv 2 \pmod{5} \Rightarrow...
So $ k = 5m + 1 $, and $ x = 7(5m + 1) + 1 = 35m + 8 $.
We now find a two-digit value of $ x $:
35m + 8 \geq 10 \Rightarrow m \geq 0, \quad 35m + 8 \leq 99 \Rightarro...
Try $ m = 0 $: $ x = 8 $ (not two-digit)
Try $ m = 1 $: $ x = 43 $

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