Question

4^61+4^62+4^63+4^64+4^65 is divisible by

a)3

b)5

c)11

d)17

Answer 1

11 ............................

Answer 2

${4}^{61} + {4}^{62} + {4}^{63} + {4}^{64} + {4}^{65} \\ = {4}^{61} (1 + 4 + {4}^{2} + {4}^{3} + {4}^{4} ) \\ = {4}^{61} (1 + 4 + 16 + 64 + 256) \\ = {4}^{61} (325 )\\ = {4}^{61} (25 \times 13) \\ = {4}^{61} \times 5 \times 5 \times 13 \\ = 5( {4}^{61} \times 5 \times 13) \\ \\ according \: to \: this \: calculation...... \\ this \: is \: devisible \: by \: 5..........$
hope this helps............