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How to find the value of the unknown in the equations . I have tried finding the value y by equating the left hand side to the right hand side $\;20\pmod 9 = y\pmod6$, find the value of $y$

Bernard
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Mickey
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  • The equation makes no sense as written. Maybe you mean $,20\bmod 9,=, y\bmod 6$ ? Please clarify. Where does the equation come from? – Bill Dubuque Dec 08 '18 at 22:33

1 Answers1

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Hint:

First of all, reduce the equation: as $20\equiv 2\mod 9$, the equation is $$ˆy\mod 6= 2\mod 9$$ Next, translate what it means in a concrete way: there exist $k,\ell\in \mathbf Z$ such that $$y+6k=2+9\ell\iff y=2+9\ell-6k.$$ Last: think of Bézout's identity.

Bernard
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