Math  /  Algebra

Question(vii) 84x438y=15084 x-438 y=150.
Having that gcd(a,b)=1\operatorname{gcd}(a, b)=1, prove the following: (i) gcd(2a+b,a+2b)=1\operatorname{gcd}(2 a+b, a+2 b)=1 or 3 . (ii) god(a+b,a2+b2)=1\operatorname{god}\left(a+b, a^{2}+b^{2}\right)=1 or 2 .
For a,bZ+a, b \in \mathbf{Z}^{+}, and n1n \geq 1, prove that if anbna^{n} \mid b^{n}, then aba \mid b

Studdy Solution
لإثبات أنه إذا كان anbna^n \mid b^n فإن aba \mid b، نستخدم خاصية القواسم. إذا كان ana^n يقسم bnb^n، فإن aa يجب أن يقسم bb لأن القوى لا تغير القواسم الأساسية.

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