SOLUTION: Find the sum of all prime numbers between 1 and 100 that are simultaneously 1 greater than a multiple of 4 and 1 less than a multiple of 5.

Question 21268: Find the sum of all prime numbers between 1 and 100 that are simultaneously 1 greater than a multiple of 4 and 1 less than a multiple of 5.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
1.LET ANY INTEGER BE N
FOURTIMES THAT =4N
ONE GREATER THAN THAT = 4N+1
2.LET ANY INTEGER BE M
FIVE TIMES THE NUMBER =5M
ONE LESS THAN THAT =5M-1
3. THE NUMBER HAS TO SATISFY BOTH CONDITIONS AND IT HAS TO BE A PRIME NUMBER.SO THE NUMBER SHOULD BE SUCH THAT
4N+1=5M-1=P SAY WHERE P IS THE REQUIRED PRIME NUMBER.
HENCE LET US TRY N=1,2,3...ETC ,WE GET FIRST NUMBER AS 4*7+1=29 WHICH SATISFIES 5*6-1=29 CRITERIA.
NEXT IS 4*22+1=89 AND 5*18-1=89
SO THEIR SUM IS 29+89=118

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