Question 13382: if 2x+1 is a multiple of 5,and if 2x+1<100, how many possible values of x are prime numbers
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! [qoute]
if 2x+1 is a multiple of 5,and if 2x+1<100, how many possible values of x are prime numbers [/quote]
Sol: Note2x+1 is odd, if 2x+1 = 5q for some positive integer q.
then q must be odd. We can set q = 2k -1 for some psitive integer k.
Hence,if 2x+1 = 5(2k-1) = 10 k -5 ,then x = 5k -3. (why?)
Since 2x+1 <100 and x ( >0)is prime , so x = 5k -3 <= 49 or 5k <= 52.
k start from 1, 2,4...,up to 10 as
(to make x to be prime,k is not odd >1 ormultiple of3)
k | x = 5k-3
---------------
1 | 2 (prime(OK)
2 | 7 (prime(OK)
4 | 17 (prime(OK)
8 | 37 (prime(OK)
10 | 47 (prime(OK)
Hence, there are 5 such primes x with 0< 2x+1 < 100 and (2x+1) = 0 mod 5.
The above solution is the shortest way to get the answer withour redundant
testing.
Sorry, I won't give further explanations.
Try to read carefully to understand the details.
Kenny
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