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

Answer:

62

Step-by-step explanation:

we have given $a> 2$

then $\frac{2}{a}\ ,\frac{3}{a+1}\ ,\frac{4}{a+2}\ , \frac{5}{a+3}\ ,\frac{6}{a+4}$

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