Question

$7^9+9^7$ is divisible by

• A. $128$
• B. $24$
• C. $64$
• D. $72$

Answer 1

The correct option is C $64$

$7^9+9^7={(8-1)}^9+{(8+1)}^7$

$=[{{}^{9}C}_0{8}^9-{{}^{9}C}_1{8}^8+{{}^{9}C}_2{8}^7-.....+{{}^{9}C}_8{8}^1-{{}^{9}C}_9(1\left)\right]+[{{}^{7}C}_0{8}^7+{{}^{7}C}_1{8}^6+{{}^{7}C}_2{8}^5+.....+{{}^{7}C}_6{8}^1+{{}^{7}C}_7(1\left)\right]$

$=8^{2}k+72-1+56+1=8^{2}k+128=8^2(k+2)$

which is divisible by $64$