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how to add card to apple wallet - All Square Golf

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 Question: What is the largest integer that must divide the product of any five consecutive integers in a genetic sequence?

📌 Question: How many integers between 1 and 100 are congruent to 3 modulo 7?

📌 Question: What is the smallest positive integer that is a multiple of 15 and one less than a multiple of 4?

📌 Let $ a = x - y $ and $ b = x + y $, so $ ab = 2025 $. Since $ x $ and $ y $ are integers, $ a $ and $ b $ must both be integers, and both must be either even or odd to ensure $ x =

📌 The number of positive divisors is $ (4+1)(2+1) = 15 $. So there are 15 positive divisor pairs $ (a, b) $ with $ ab = 2025 $. Including negative divisors, we have $ 30 $ total integer pairs $ (a, b) $.

📌 But we must ensure $ a $ and $ b $ are both odd. Note that $ 2025 $ is odd, so all its divisors are odd. Hence $ a $ and $ b $ are both odd, so $ a + b $ and $ b - a $ are even, and $ x, y $ are integers. Therefore, every divisor pair yields a lattice point.

📌 Each such pair $ (a, b) $ gives a unique solution:

📌 Since $ (a, b) $ and $ (-a, -b) $ give different points (as $ x, y $ change sign appropriately), all 30 pairs yield valid lattice points.

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