Question

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solve it. ▬▬▬▬▬ஜ۩۞۩ஜ▬▬▬▬▬​

Answer 1

Answer:

p is a prime no greater than 3

that is 5, 7, 11,13, 17,19,...

we have to find general term

take it as 2 series

5,11,17,.....

7,13,19,....

For 5,11,17,... general term

= 6n -1 ( common difference 6)

for 7,13,19,....

general term = 6n +1 ( same difference 6 but first term 7 So add 2 to 6n-1)

Now,( p^2 +17 )/12

take 6n +1 term

(6n+1)^2 +17)/12

= 36 n^2 + 1 + 12n +17)/12

= 36n^2 +12n +18)/12

Now as n is integer and 36 is divisible by 12

so 36 n^2/12 =>3n^2 is divisible by 12

12n obviously it is divisible

So , Now 18/12

=1 + 6/12

So, remainder = 6

So, (1) option is correct

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