We say (a, b, c) is a Pythagorean Triple if a, b, c are positive integers and a? 3² = c². For example, (3, 4, 5) and (5, 12, 13) are Pythagorean triples. Assume that (a, b, c) is a Pythagorean triple in which the only common divisors of a, b, c are ±1. 1. Show that a and b cannot both be odd. 2. Assume that a is even. Show that there exist relatively prime integers m and n so that а %3 2тп, b %3D т? — п?, аnd c %3 т? + п?. Hint: Factor a² = c² – b² after showing that (c+b, c – b) = 2.

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A: Given :    5 raised to the power of 1

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A: conjugate is where we change the sign in the middle of two terms . So ,conjugate is 3+2√5

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A: SUm of infinite terms of G.P. isa1-r

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A: In Hindu-Arabic standard form of an expression 2×103+5=2×1000+5=2005

Q: Discrete Math: Q1: a) Find 8 + 32 + 126 + … + 8192.       b) Find 5 + 15 + 45 + · · · + 5·3^20…

A: Now we know that sum of n terms of GP is given by Sn=a*(r^n−1)/(r−1) when r>1

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