(A) Prove or Disprove: If a ≡ B (Mod 5) $a ^ { 2 } \equiv b ^ { 2 } ( \bmod 5 )$

question 27

Essay

(a) Prove or disprove: If a ≡ b (mod 5), where a and b are integers, then $a ^ { 2 } \equiv b ^ { 2 } ( \bmod 5 )$ (b) Prove or disprove: If $a ^ { 2 } \equiv b ^ { 2 } ( \bmod 5 )$ where a and b are integers, then a ≡ b (mod 5).

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Definitions:

Chloride

A chemical element that, when combined with sodium, forms table salt (sodium chloride), and plays vital roles in bodily functions.

Magnesium

A chemical element with the symbol Mg and atomic number 12, essential for human health, involved in over 300 biochemical reactions in the body.

Laboratory Value

A numerical result obtained from a laboratory test that measures specific markers in blood, urine, or other body fluids, used to assess health or diagnose conditions.

Calcium

A chemical element and a vital mineral in the human body necessary for bone health, muscle function, and nerve signaling.