3sry bhaiyya
n is a prime number greater than 3
bhaiyya plz post the solution
if n is number greater than 3, show that n2-1 is a multiple of 24.
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5 Answers
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11The given number is divsible both by 8 and by 3.
Because from totient theorem, n^2\equiv 1(mod3) \Rightarrow 3|(n^2-1).
Also odd squares are of the form 8k+1, meaning (n2-1)=8k.
Done.
1357This can be done by the fact that if the number is prime then it is of the from 6k + 1 or 6k -1
Then it is simple..
Can you complete the proof from here?
1357One more method that can be by observation
take 3 consecutive numbers n-1,n,n+1
given n is prime, so n-1, n+1 are even.
Out of these 3 consecutive numbers one number is divisible by 4, one is divisible by 3 and one is divisible by 2.
so (n-1)(n)(n+1) is divisible by 4*3*2=24
now since n is prime, (n-1)(n+1) is divisible by 24.
3it becomes very easy when we apply fermats theorem bhaiyya.
i did this way only,making factors and and applying theorem and divisibility property of 3 consecutive numbers.