Suppose there are integers ๐๐, ๐๐, ๐ฅ๐ฅ and ๐ฆ๐ฆ such that ๐๐ฅ+๐๐ฆ=5๐๐ฅ+๐๐ฆ=5, and 55 does not divide ๐ฅ๐ฅ. What is gcd(๐ฅ,๐ฆ)gcd(๐ฅ,๐ฆ)?
Question
Solution 1
The given equation is ax + by = 5.
The greatest common divisor (gcd) of two numbers is the largest number that divides both of them without leaving a remainder.
In this case, we are asked to find the gcd of x and y.
From the given equation, we can see that both x and y are factors of 5.
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Suppose there are integers ๐๐, ๐๐, ๐ฅ๐ฅ and ๐ฆ๐ฆ such that ๐๐ฅ+๐๐ฆ=5๐๐ฅ+๐๐ฆ=5, and 55 does not divide ๐ฅ๐ฅ. What is gcd(๐ฅ,๐ฆ)gcd(๐ฅ,๐ฆ)?
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