Putting n=1
We get
"9-5=4"
Which is divisible by 4 so 4 is the factor of 4
Let
"T(k) =9k-5k=4m\\ for \\ some \\ m" is true "\\ \\ \\ \\ ....(1)"
For
"T(k+1)"
Now,
"=4(m+1)"
Thus, "T(k+1)" is divisible by 4, hence 4 is a factor of it. By the principle of mathematical induction, 4 is a factor of 9n-5n for all integers "n \\geq 1."
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