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

  • Context: High School 
  • Thread starter Thread starter Superposed_Cat
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Discussion Overview

The discussion revolves around solving the equation X = Y%Z for Y, exploring various values and conditions that satisfy this equation. Participants examine specific examples and seek to derive a general formula applicable to different scenarios.

Discussion Character

  • Exploratory, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents an example where x=3, z=9, and y=12, suggesting that multiple values for y can satisfy the equation.
  • Another participant proposes a formula y=z*i+x, where i is an integer greater than 0, to express possible values for y.
  • A different participant questions the restriction of i being greater than 0, providing an example of -6 satisfying the equation, indicating that negative integers can also be valid.
  • Further clarification is offered that y can be expressed as y=nz+x for any integer n, suggesting a broader range of solutions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the conditions for i or n, with differing views on the inclusion of negative integers and the generality of the proposed formulas.

Contextual Notes

The discussion highlights the dependence on integer definitions and the implications of modular arithmetic, with unresolved aspects regarding the completeness of the proposed formulas.

Superposed_Cat
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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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