How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Question

loser66 · Answer

exactly the same with the question above , take a look at http://openstudy.com/users/terenzreignz#/updates/51a32efee4b00f621d792b53

raden · Answer

shortly, try this
lcm(13,26) = 26
floor(1000/26) = 38
so, it is 38


another way :
Sum of 26 consecutive integers can be written as (-351+26a) 

1<= -351+26a <= 1000
352 <= 26a <= 1351
13.5 <= a <= 51.96

Sum of 13 consecutive integers can be written as (-91+13b)

7.07 <= b <= 83.92

Accordingly informations above 
-351+26a = -91+13b 
26a-13b = 260
2a-b = 20 
b = 2a-20

a = (14,15,....51) satisfies it. 
So total 38 numbers

anonymous · Answer

Given that sin(2θ)=2/3, the value of

sin^6θ+cos^6θ
can be written as a/b with a and b coprime positive integers. what is a+b?

ganeshie8 · Answer

start by simplifying  sin^6θ+cos^6θ

anonymous · Answer

What is the smallest 3-digit number which comprises of 3 distinct digits?

ganeshie8 · Answer

what do u think :)