Posted by ianian on .
Consider all 3term geometric sequences with first term 1 and with common ratio the square of an integer between 1 and 1000. How many of these 1000 geometric sequences have the property that the sum of the 3 terms is prime?

Maths 
Reiny,
so we are looking for
1 + x^2 + x^4 being a prime
x^4 + x^2 + 1
= x^4 + 2x^2 + 1  x^2
= (x^2 + 1)^  x^2  a difference of squares
= (x^2 + 1 +x)(x^2 + 1 x)
if x = 1 , we get
(1+1+1)(1) = 3  a prime number
for any other value of x, the value of each bracket > 1
and 1+x^2 + x^4 is the product of at least two factors
thus : 1 + 1^2 + 1^4 is the only such case
1 1 1 is the only case 
Maths 
tsong,
111 is incorrect

Maths 
PD,
@Tsong, the answer is not 111, the answer is 3 :P

Maths 
PD,
sorry, the answer is 1 :P

Maths 
abc,
thanxxxx