How to Solve for Y in the Equation X = Y%Z?

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To solve for y in the equation x = y%z, the formula can be expressed as y = nz + x, where n is any integer. This allows for multiple valid y values that satisfy the equation, including negative values. For example, if x = 3 and z = 9, possible y values include 12, 3, 21, and -6. The discussion emphasizes that n must be an integer greater than 0 to generate positive values, but the broader formula accommodates all integers. The key takeaway is that y can take on an infinite number of values based on the integer n.
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Hey all, if x=y%z How do i solve for y?
 
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Superposed_Cat said:
Hey all, if x=y%z How do i solve for y?
Take an example:

3=12\%9

So in this case we have that x=3, z=9, and y=12. But also,

3=3\%9
3=21\%9
3=-6\%9
3=(100*9+3)\%9

Are you seeing the pattern? Can you develop a simple formula that gives us every possible y value that satisfies this equation?
 
y=z*i+x, i is int > 0
 
Why greater than 0? -6= 3%9 because -6= 3+ (-1)9.

(I would say "-6= 3 (mod 9). "%" is computer code.)
 
HallsofIvy said:
Why greater than 0? -6= 3%9 because -6= 3+ (-1)9.
Yes, ## y = nz+x## ##∀x,y,z,n ∈ ℤ ## is more inclusive.
 

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