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Home » 2! The Ultimate PEMDAS Guide That Every Student Must Know Now - Appcentric

2! The Ultimate PEMDAS Guide That Every Student Must Know Now - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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We solve the system of congruences:
N \equiv 3 \pmod{4} \\
N \equiv 2 \pmod{5} \\
N \equiv 4 \pmod{7}
Start with the first two:
Step 1: Solve \( N \equiv 3 \pmod{4} \) and \( N \equiv 2 \pmod{5} \)
Let \( N = 4a + 3 \). Substitute into second:
4a + 3 \equiv 2 \pmod{5} \Rightarrow 4a \equiv -1 \equiv 4 \pmod{5} \R...
So \( a = 5b + 1 \), then \( N = 4(5b + 1) + 3 = 20b + 7 \)
Thus, \( N \equiv 7 \pmod{20} \)

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