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Home » Thus, the number of distinct sequences is $\boxed326592$. - RTA

Thus, the number of distinct sequences is $\boxed326592$. - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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Question: What two-digit positive integer is one less than a multiple...
Solution: Let $ x $ be the two-digit number.
x \equiv -1 \pmod{9} \quad \text{and} \quad x \equiv 1 \pmod{7}
Rewriting:
x = 9k - 1 \quad \text{for some } k
Substitute into the second congruence:
9k - 1 \equiv 1 \pmod{7} \Rightarrow 9k \equiv 2 \pmod{7}
Since $ 9 \equiv 2 \pmod{7} $, this becomes:
2k \equiv 2 \pmod{7} \Rightarrow k \equiv 1 \pmod{7}
So $ k = 7m + 1 $, and:

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