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Home » Wilford, North Yorkshire, village and civil parish in England - Groen Casting

Wilford, North Yorkshire, village and civil parish in England - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 4^2 = 16 \equiv 1 \pmod{15}? \quad 16 - 1 = 15 \equiv 0 \pmod{15} \Rightarrow \text{Yes.}

📌 Thus, the smallest positive integer \( n \) is:

📌 An ornithologist uses GPS tracking to study a flock of geese whose flight paths form a repeating cycle every \( k \) days. She observes that a particular behavioral pattern occurs every \( k \) days, where \( k \) is the smallest two-digit number such that \( k \) is divisible by the sum of its digits and leaves a remainder of 2 when divided by 7. What is \( k \)?

📌 We seek the smallest two-digit number \( k \) such that:

📌 \( k \equiv 2 \pmod{7} \),

📌 \( k \) is divisible by the sum of its digits.

📌 Let \( k = 10a + b \), where \( a \in \{1,2,\dots,9\} \), \( b \in \{0,1,\dots,9\} \), so sum of digits is \( a + b \).

📌 We check two-digit numbers \( k \equiv 2 \pmod{7} \): they are:

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