Question

if a is divisible neither 2 nor 3 show that a2-1 is divisible by 24
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Answer 1

Answer:

yes there multiple by 3

Answer 2

• If a number is divisible neither by 2 nor 3 then it is also not divisible by 3*2 = 6. Then a must of the form 6n+1 or 6n-1. As 6n+2,6n+3,6n+4 is divisible by either 2 or 3.
• So a²-1 = $(6n+1)^{2} or (6n-1)^{2} = 36n^{2}$ ± 12n
• this implies to  12n(3n±1).

• So this is divisible by 12 as 12 is a factor. Now n or 3n±1 will be an even number. So the whole is divisible by 2*12 = 24

• So a²-1 will be divisible by 24.