Question

Find the smallest integer a > 2 such that 2/a, 3/a+1, 4/a+2, 5/a+3, 6/a+4

Answer 1

62

Explanation:

we have given
`a> 2`

then
`(2)/(a)\ ,(3)/(a+1)\ ,(4)/(a+2)\ , (5)/(a+3)\ ,(6)/(a+4)`

since it is given that
`a> 2`

so
`a\equiv 2\ mod\ 4`
`a\equiv 2\ mod\ 5`
`a\equiv 2\ mod\ 6`

`a\equiv2 \left ( mod\ 2,3,4,5,6 \right )`

`a\equiv2 \left ( mod\ lcm\left ( 2,3,4,5,6 \right )\right )`

`a\equiv2 \left ( mod\ 60 \right )`

then a=60n+2 where n is a positive integer

so smallest value of a is a=60×1+2=62