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Home » \frac210495 = \frac1433 - Dachbleche24

\frac210495 = \frac1433 - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 We are to find the smallest such $ n > 50 $. Try $ k = 1 $:

📌 n = 77 \cdot 1 + 1 = 78

📌 Since $ 78 > 50 $, this is valid.

📌 Therefore, the smallest clutch size greater than 50 that satisfies the conditions is:

📌 \boxed{78}

📌 Question: An ichthyologist notes that the population sizes of two fish species in a reef, $ a $ and $ b $, satisfy $ a + b = 1000 $, and both are divisible by the same prime number $ p $. What is the largest possible value of $ p $?

📌 We are given that $ a + b = 1000 $, and $ p \mid a $, $ p \mid b $, so $ p \mid (a + b) = 1000 $. Therefore, $ p $ must be a prime divisor of 1000.

📌 Factor 1000:

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