Fill in the blanks... 1) if \"a\" is a positive integer, then gcd(a,a+2)=_______

Question

Fill in the blanks...

1) if "a" is a positive integer, then gcd(a,a+2)=_______________
2) if gcd(120,b)=8, then b=_______________
3) if "a" is a positive integer, then gcd(a,a^2)=_______________
4) if gcd.(a,b)=1, then gcd(2a-3b,4a-5b)|?______________
5) if gcd.(a,b)=1, then gcd(2a+3,4a+5)=_______________1?
6) the 3rd term in the binomial expansion of (2a-b)^4 is_____________

Explanation / Answer

1) gcd( a, a+2) = a 2) gcd(120,b) =8 , => b = 15 3) gcd( a , a^2) =a 4) gcd(a, b) =1 , gcd(2a-3b,4a-5b) = 1 5) gcd.(a,b)=1, then gcd(2a+3,4a+5)=1 6) 4C3 (2a)^3 (-b)

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