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To verify $a \equiv b \pmod{n}$, divide $a$ by the modulus $n$ using long division and check if the remainder is $b$. If the remainder matches $b$, the congruence is valid.

Conditions: The method is demonstrated for positive dividends and positive moduli.; The speaker calls it a colloquial explanation.

To verify $a \equiv b \pmod{n}$, divide $a$ by the modulus $n$ using long division and check if the remainder is $b$. If the remainder matches $b$, the congruence is valid.

Conditions: The method is demonstrated for positive dividends and positive moduli.; The speaker calls it a colloquial explanation.

Congruence ($\equiv$) indicates that two numbers have the same remainder when divided by a modulus, whereas equality ($=$) means they are the exact same integer. The video uses congruence in cryptography instead of equality.

Conditions: Used in modular arithmetic contexts.; The modulus is explicitly shown in the examples (e.g., mod 12).

Congruence ($\equiv$) indicates that two numbers have the same remainder when divided by a modulus, whereas equality ($=$) means they are the exact same integer. The video uses congruence in cryptography instead of equality.

Conditions: Used in modular arithmetic contexts.; The modulus is explicitly shown in the examples (e.g., mod 12).

The video states that modular arithmetic is a central mathematical concept in cryptography and that widely used cryptographic algorithms mainly depend on it.

Conditions: This is a motivational claim stated by the video.; No specific algorithm is named in this segment.

The video states that modular arithmetic is a central mathematical concept in cryptography and that widely used cryptographic algorithms mainly depend on it.

Conditions: This is a motivational claim stated by the video.; No specific algorithm is named in this segment.