Use mathematical induction to prove that $4 \mid \left( 9 ^ { n } - 5 ^ { n } \right)$ for all $n \geq 0$

Question

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The Answer is P(0): 4 $P(0): 4 1-1 is true since 4 0 . P ( k ) ightarrow P ( k + 1 ) : 9 ^ { k + 1 } - 5 ^ { k + 1 } = 9 \left( 9 ^ { k } - 5 ^ { k } ight) + 5 ^ { k } ( 9 - 5 ) . each term is divisible by \left. 4 : 4 \mid 9 ^ { k } - 5 ^ { k } ext { (by } P ( k ) ight) ext { and } 4 \mid 9 - 5$ 1-1 is true since 4 $P(0): 4 1-1 is true since 4 0 . P ( k ) ightarrow P ( k + 1 ) : 9 ^ { k + 1 } - 5 ^ { k + 1 } = 9 \left( 9 ^ { k } - 5 ^ { k } ight) + 5 ^ { k } ( 9 - 5 ) . each term is divisible by \left. 4 : 4 \mid 9 ^ { k } - 5 ^ { k } ext { (by } P ( k ) ight) ext { and } 4 \mid 9 - 5$ 0 .

P ( k ) ightarrow P ( k + 1 ) : 9 ^ { k + 1 } - 5 ^ { k + 1 } = 9 \left( 9 ^ { k } - 5 ^ { k } ight) + 5 ^ { k } ( 9 - 5 )

. each term is divisible by

\left. 4 : 4 \mid 9 ^ { k } - 5 ^ { k } ext { (by } P ( k ) ight) ext { and } 4 \mid 9 - 5

Use Mathematical Induction to Prove That 4∣(9n−5n)4 \mid \left( 9 ^ { n } - 5 ^ { n } \right)4∣(9n−5n)

Use Mathematical Induction to Prove That $4 \mid \left( 9 ^ { n } - 5 ^ { n } \right)$