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18 Jun 2018, 21:06
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longhaul123
Hello
In general when we talk about multiples/factors, we talk about non-zero positive integers only. This is how multiples/factors are defined in my opinion.
27 Jun 2018, 23:36
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did you mean to say that since 0 is a multiple of every integer then 0 can have any factors including 4 . Since the question is stressing on the point that it is just a multiple of 4 so 0 cant be considered.
SchruteDwight
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12 Dec 2018, 01:52
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[quote="stonecold"]A lot of solutions on this page already.
Here is mine
Clearly both 1 and 2 are alone insufficient.
combining them => x=4a y=4b and a=b+1 where b and b+1 will always be coprimes.
stonecold
how do you get a=b+1
If I understand it correctly,
Your solution is as follows:
S1) x=4a, y=4b
S2) x-y=4
S1) & S2) 4(x-y)=4 –> x-y=1 –> 4a-4b=1 –> a=b+1
Since a>b –> gcd(x,y)=gcd(4*(b+1), 4b)=gcd(4b+4-4b,4b)=gcd(4,4b)=4
Here is mine
Clearly both 1 and 2 are alone insufficient.
combining them => x=4a y=4b and a=b+1 where b and b+1 will always be coprimes.
stonecold
how do you get a=b+1
If I understand it correctly,
Your solution is as follows:
S1) x=4a, y=4b
S2) x-y=4
S1) & S2) 4(x-y)=4 –> x-y=1 –> 4a-4b=1 –> a=b+1
Since a>b –> gcd(x,y)=gcd(4*(b+1), 4b)=gcd(4b+4-4b,4b)=gcd(4,4b)=4
