There is more than one integer, greater than 1, which leaves a remainder of 1 when divided by each of the four smallest primes. What is the difference between the two smallest such integers?
Answers
Given : There is more than one integer, greater than 1, which leaves a remainder of 1 when divided by each of the four smallest primes
To find : the difference between the two smallest such integers
Solution:
Four Smallest Primes
2 , 3 , 5 , 7
Number When Divided by 2 , 3 , 5 & 7 Leaves remainder 1
Hence N = 2a + 1
N = 3b + 1
N = 5c + 1
N = 7d + 1
=> N - 1 = 2a = 3b = 5c = 7d
as 2 , 3 , , 5 & 7 are co prime
Hence
N - 1 = 2 * 3 * 5 * 7
=> N - 1 = 210
=> N = 211
Next N - 1 = 2(210)
=> N - 1 = 420
=> N =421
Difference = 421 - 211 = 210
difference between the two smallest such integers = 210
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