Question

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?

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

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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