Question

exactly two of the divisors of 3^8-1 are between 5 and 20, what is the product of these two divisors

Answer 1

Step-by-step explanation:

332-1=(3-1)(3+1)(32+1)(34+1)(38+1)(316+1)

Answer 2

Solution :-

→ 3⁸ - 1

→ 3⁸ - 1⁸

→ (3⁴)² - (1⁴)²

→ (3⁴ + 1)(3⁴ - 1⁴)

→ (3⁴ + 1){(3²)² - (1²)²}

→ (3⁴ + 1)(3² + 1)(3² - 1)

→ (3⁴ + 1)(3² + 1)(3 + 1)(3 - 1)

→ (81 + 1) * (9 + 1) * 4 * 2

→ 82 * 10 * 8

So,

→ Divisors between 5 and 20 = 8 and 10

→ Required product = 8 * 10 = 80

Also,

→ 82 * 10 * 8

→ 2 * 41 * 10 * 8

→ 41 * 10 * 2 * 8

→ 41 * 10 * 16

So,

→ Divisors between 5 and 20 = 10 and 16

→ Required product = 10 * 16 = 160 .

Learn more :-

solution of x minus Y is equal to 1 and 2 X + Y is equal to 8 by cross multiplication method

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