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# Number Theory

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For all positive integers n, the nth triangular number T_n is defined as T_n = 1 + 2 + ... + n . What is the greatest possible value of the greatest common divisor of 4T_n and n - 2?

Dec 23, 2021

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use the Euclidean algorithm to find $$\gcd(4\cdot\frac{n(n+1)}{2}, n-2)$$