Most Students Guess… | Math Olympiad
Автор: Math Hacks Hub
Загружено: 2026-02-21
Просмотров: 101
Описание:
Math Olympiad Challenge — A Deceptively Simple Equation!
5/a + 6/b = 7
Find a and b, where a and b are positive integers (ℤ⁺)
At first this looks like a basic algebra problem.
But here's the catch — there are infinitely many real
solutions, yet only TWO whole number solutions exist.
The question is: how do you find them WITHOUT trial and error?
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🧠 What You'll Learn:
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✔️ How to rearrange the equation to express b in terms of a
✔️ Why (7a - 5) must divide 30 — the key insight
✔️ How to systematically test all divisors of 30
✔️ Why only a = 1 and a = 5 survive as valid positive integers
✔️ A powerful number theory technique reusable across
dozens of Olympiad problems
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📌 Try It Yourself First!
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Pause before the solution — can you find BOTH
(a, b) pairs using logic, not guessing?
Drop your answers in the comments below! 👇
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🔔 Subscribe for daily Olympiad problems, number
theory tricks, and competition math strategies that
build real mathematical instincts from the ground up.
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#MathOlympiad #NumberTheory #AlgebraChallenge
#OlympiadMath #CompetitionMath #DivisibilityTrick
#PositiveIntegers #MathTrick #MathProblemSolution
#BrilliantMath
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