Question 36211: a) For any prime p>=5, prove that p2+2 ( P square +2) is composite or not.
b) Find the smallest number n, which has the following properties:
1).Its decimal represenation has 4 as the last digit;
2).It is divisible by 3 and 8.
3).Its a square number
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! a) For any prime p>=5, prove that p2+2 ( P square +2) is composite or not.
IT IS COMPOSITE
AT P=5,WE HAVE P^2+2=5^2+2=25+2=27..IVISIBLE BY 3 AN 9.
AT P=6,WE HAVE P^2+2=6^2+2=38...DIVISIBLE BY 2,19.
b) Find the smallest number n, which has the following properties:
1).Its decimal represenation has 4 as the last digit;
2).It is divisible by 3 and 8......LCM OF 3 AND 8 IS 24.
HENCE ANSWER SHOULD BE` A MULTIPLE OF 24
24*1=24...NOT A PERFECT SQUARE
.....
....
24*6=144..IS A PERFECT SQUARE AND IT HAS 4 AT THE END
SO 144 IS THE ANSWER.
3).Its a square number
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