Modular Arithmetic and Algebra

Given:

$\large{4096 x = 61741 + 15625 y}$

$\text{-x and y are integers}$

$\text{-y is not divisible by 5}$

$x = \dfrac{61741 + 15625y}{4096}$

$61741 + 15625y \equiv 0 \pmod{4096}$

$15625y \equiv -61741 \pmod{4096}$

$15625y \equiv -61741 + 4096 \equiv -57645 \pmod{4096}$

$3125y \equiv -11529 \pmod{4096} \text{ [divide 5] }$

$3125y \equiv -11529 - 4096 \equiv -15625 \pmod{4096}$

$y \equiv -5 \equiv 4091 \pmod{4096}$

$\text{Minimum positive values:} y = 4091, x = 15621$

#NumberTheory

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$