+0  
 
0
60
2
avatar

Let S = 1 + 2 + 3 + ... + 2010. What is the residue of S, modulo 2010?

 Nov 21, 2021
 #1
avatar
0

1 + 2 + 3 + 4 +.........+ 2010 ==[2010 x 2011] / 2==2,021,055 mod 2010==1,005 - the remainder

 Nov 21, 2021
 #2
avatar+306 
+2

Alternative solution:

Pair the numbers up as follows

1 2010
2 2009
3 2008
4 2007
5 2006
...  
1004 1007
1005 1006

We can see that there are 2010/2=1005 rows, and the sum of each row is 2011, which is equal to 1 modulo 2010, thus the answer is

1005*1 = 1005

Hope this helped :)

 Nov 21, 2021

15 Online Users

avatar
avatar
avatar