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-13^{-1} \mod83

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(−13⁻¹)mod 83

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(−13⁻¹) mod 83

Modulo Definition

a mod b is the remainder from the division of a by b

Apply modulo rule: (−a) mod b = (− (a mod b)) mod b

=(−(13⁻¹ mod 83)) mod 83

Find Modular multiplicative Inverse: 13⁻¹ mod 83=32

Apply modulo rule: (a^(−b)) mod c = ((a⁽⁻¹⁾ mod c)^b) mod c

=(−(32¹ mod 83)) mod 83

32¹=32

=(−(32 mod 83)) mod 83

32 mod 83: 32

=(−32) mod 83

If |a|<b and a < 0 then a mod b = a+b

=−32+83

=51

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(−13)⁻¹mod 83

−13⁻¹mod 83

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

-13^{-1} \mod83

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