(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).

---

Definitions:

Chemical Reactions

Processes in which one or more substances are chemically changed into one or more new substances.

Pyrogens

Substances that cause fever by acting on the hypothalamus's temperature-regulating center.

Adipose Stores

Adipose stores refer to the body's fat reserves, primarily stored in adipose tissue, which provides insulation and energy.

Depolarization Phase

Change in the electric charge difference across the plasma membrane that causes the difference to be smaller or closer to 0 mV; phase of the action potential in which the membrane potential moves toward zero, or becomes positive.