Understanding this proof for the proposition "For all integers a, gcd (9a+4, 2a+1) = 1.

Proof: gcd (9a+4, 2a+1) = gcd (2a+1, a) = gcd (a, 1). Since gcd (a, 1) = 1, gcd (9a+4, 2a+1) = 1.

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Mathematics

Rishi Schmidt

14 February, 22:01

Understanding this proof for the proposition "For all integers a, gcd (9a+4, 2a+1) = 1.

Proof: gcd (9a+4, 2a+1) = gcd (2a+1, a) = gcd (a, 1). Since gcd (a, 1) = 1, gcd (9a+4, 2a+1) = 1.

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Answers (1)

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Tucker Hoover · Answer 1

First line because 4 (2a+1) = 8a+4 and 9a+4 - (8a+4) = a

Second line because a times 2 = 2a and 2a+1-2a=1

Although the second equality is more or less obvious since 2a+1 leaves a remainder of 1 when divided by a.

Understanding this proof for the proposition "For all integers a, gcd (9a+4, 2a+1) = 1.Proof: gcd (9a+4, 2a+1) = gcd (2a+1, a) = gcd (a, 1). Since gcd (a, 1) = 1, gcd (9a+4, 2a+1) = 1.

Understanding this proof for the proposition "For all integers a, gcd (9a+4, 2a+1) = 1.

Proof: gcd (9a+4, 2a+1) = gcd (2a+1, a) = gcd (a, 1). Since gcd (a, 1) = 1, gcd (9a+4, 2a+1) = 1.