Understanding Congruence and Powers of Two

The video tutorial explains how to find the remainder when 2^124 is divided by 7 using congruence. It starts by determining congruences for powers of two modulo 7, then expresses 2^124 using factors of 2^3. By simplifying the expression, it concludes that the remainder is 2.

What mathematical concept is used to find the remainder when 2^124 is divided by 7?

• Congruence

• Factorization

• Differentiation

• Integration

What is 2^1 congruent to modulo 7?

• 1

• 2

• 3

• 4

What is the remainder when 2^3 is divided by 7?

• 2

• 3

• 1

• 0

Why can every factor of 2^3 in 2^124 be replaced with 1?

• Because 2^3 is congruent to 0 mod 7

• Because 2^3 is congruent to 1 mod 7

• Because 2^3 is congruent to 2 mod 7

• Because 2^3 is congruent to 3 mod 7

How can 2^124 be expressed using factors of 2^3?

• 2^3 raised to the power of 43

• 2^3 raised to the power of 40

• 2^3 raised to the power of 42

• 2^3 raised to the power of 41

Which property of exponents is used to express 2^124 in terms of 2^3?

• a^0 = 1

• (a^m)^n = a^(m*n)

• a^m / a^n = a^(m-n)

• a^m * a^n = a^(m+n)

What is the quotient when 124 is divided by 3?

• 41

• 43

• 42

• 40

What is the remainder when 124 is divided by 3?

• 2

• 1

• 3

• 0

What is the significance of the remainder being 1 when dividing 124 by 3?

• It indicates an extra factor of 4

• It indicates an extra factor of 3

• It indicates an extra factor of 2

• It indicates an extra factor of 5

What is the final remainder when 2^124 is divided by 7?

• 3

• 1

• 0

• 2