6x + 17y = 375

Number Theory Level 3

How many solutions does the equation 6x + 17y = 375 with x, y in N have?


The answer is 4.

Kees Vugs by Kees Vugs , 87, Netherlands

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1 solution

X X
May 29, 2018

Since gcd ⁡ ( 6 , 375 ) = 3 \gcd(6,375)=3 , y y is a multiple of 3,we get y = 3 , 9 , 15 , 21 y=3,9,15,21

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The y-values are correct and the x-values can be calculated. But why y = 5x3 and not y = 6x3. I don't see the meaning of your since.

Kees Vugs - 3 years ago

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Oh,because y can not be a multiple of 2

X X - 3 years ago

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To show that your solution is difficult to onderstand I will give another Diophantic equation.

Kees Vugs - 3 years ago

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