Question

what is a number that can be divided by 3 and have a reminder of 1 , the same number and divided 4 reminder of 1 , same number divided by 5 and reminder of 1 , same number and divided by 6 and reminder of 1 , same number and divided by 7 and reminder of 1?

Answer 1

841

Answer 2

a=3q1+1
a=4q2+1
a=5q3+1
a=6q4+1
a=7q5+1

so a-1 = 3k , 4k , 5k ,6k ,7k
so a-1 =[3,4,5,6,7] k
a-1=[3,2^2,5,3*2,7] k
a-1=2^2*3*5*7 k
a-1=420k
so
a= 420 k +1
so
a = 420+1 or 2*420+1 or 3*420+1 ...
a=421 ,841 ,...