Question

$(73^{53}+83^{53})$ നെ _____ കൊണ്ട് ഭാഗിക്കുമ്പോൾ കിട്ടുന്നത്?

• A. 150
• B. 156
• C. 154
• D. 152

Answer 1

Answer:

B. 156

$(73^{53}+83^{53})$ is divided by 156.

This is based on the algebraic identity:
For any positive odd integer $n$, $(a^n + b^n)$ is always divisible by $(a + b)$.

1. Identify the form

The expression $(73^{53} + 83^{53})$ is in the form $a^n + b^n$, where:

• $a = 73$

• $b = 83$

• $n = 53$

2. Verify the exponent

The exponent $n = 53$ is an odd number. According to the property of polynomials, when $n$ is odd, $(a + b)$ is a factor of $(a^n + b^n)$.

3. Calculate the divisor

Sum the bases to find the common divisor:
$73 + 83 = 156$