show that (2n+1)3n-1 is NOT divisible by 4 for every integer [MATH]n \geq 0[/MATH] ...................................edited
2n*3n-1+3n-1-1 [MATH]\equiv[/MATH]2n(-1)-1n-1-1
2n(-1)-1n-1-1 [MATH]\equiv[/MATH] -2n-2 [MATH]\equiv[/MATH] 2n+2 [MATH]\equiv[/MATH] 2(n+1)
But this is not true as it won´t be divisible by 4 for values of n=1 and n=2.
2n*3n-1+3n-1-1 [MATH]\equiv[/MATH]2n(-1)-1n-1-1
2n(-1)-1n-1-1 [MATH]\equiv[/MATH] -2n-2 [MATH]\equiv[/MATH] 2n+2 [MATH]\equiv[/MATH] 2(n+1)
But this is not true as it won´t be divisible by 4 for values of n=1 and n=2.
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