Prove that if a and b are both even, then gcd(a, b)=gcd(a/2, b/2) [NT-Ch.2-S2.4] - Part 17

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Prove that if b = aq + r, then gcd(a, b) = gcd(a, r) [NT-Ch.2-S2.4] - Part 9 Prove that if b = aq + r, then gcd(a, b) = gcd(a, r) [NT-Ch.2-S2.4] - Part 9
Show that if d=gcd(a, b) then gcd(a/d,b/d)=1 [NT-Ch.2-S2.4] - Part 6 Show that if d=gcd(a, b) then gcd(a/d,b/d)=1 [NT-Ch.2-S2.4] - Part 6
gcd(a, b) if and only if there exist integers x, y such that 1 = ax+by [NT-Ch.2-S2.4] - Part 4 gcd(a, b) if and only if there exist integers x, y such that 1 = ax+by [NT-Ch.2-S2.4] - Part 4
There exist integers x, y such that gcd(a,b)=ax+by [NT-Ch.2-S2.4] - Part 2 There exist integers x, y such that gcd(a,b)=ax+by [NT-Ch.2-S2.4] - Part 2
Show that if gcd(a, b)=c, then gcd(a^2, b^2)=c^2 [NT-Ch.2-S2.5] - Part 10 Show that if gcd(a, b)=c, then gcd(a^2, b^2)=c^2 [NT-Ch.2-S2.5] - Part 10
Prove that if (a1,b)=(a2,b)=(a3,b)=...=(an,b), then gcd(a1a2a3...an,b)=1 [NT-Ch.2-S2.4] - Part 20 Prove that if (a1,b)=(a2,b)=(a3,b)=...=(an,b), then gcd(a1a2a3...an,b)=1 [NT-Ch.2-S2.4] - Part 20
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