For how many natural numbers x, is the expression: (x ² + 2x + 3) divisible by 35 ?

Just to make things clear, we can calculate the last digit of x²+2x+3 for any possible natural x.
x can end in 0,1,2,3,4,5,6,7,8,9.
x² will end in 0,1,4,9,6,5,6,9,4,1 respectively.
2x will end in 0,2,4,6,8,0,2,4,6,8 (also respectively).
Adding these together with 3 yields 3,6,1,8,7,8,1,6,3,2 as the whole expression's last digit.
This means that the expression cannot be divided by 5, much less by 35 ;)

Posted by zaphod on 2004-01-07 03:19:36