Posted by ianian on Monday, April 29, 2013 at 4:13am.
Consider all 3-term 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, Monday, April 29, 2013 at 8:26am
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, Monday, April 29, 2013 at 11:13am
111 is incorrect
- Maths - PD, Tuesday, April 30, 2013 at 2:57pm
@Tsong, the answer is not 111, the answer is 3 :P
- Maths - PD, Tuesday, April 30, 2013 at 2:58pm
sorry, the answer is 1 :P
- Maths - abc, Saturday, May 4, 2013 at 2:57am
Answer this Question
More Related Questions
- algebra - Consider all 3-term geometric sequences with first term 1 and with ...
- Math - Consider all 3-term geometric sequences with first term 1 and with common...
- Maths - Eric thinks of 2 sequences.One is geometric and the other arithmetic....
- Maths - 1..The first 2 terms of a geometric progression are the same as the ...
- check! - If the third and ninth temr of a geometric series with a positive ...
- Geometric progression - The second term of a geometric progression is 12 more ...
- Mathematics. Geometric sequences. - 2+4+8+...is a geometric sequence. Prove the ...
- math... - how can I tell if a sequences is airthmetic, geometric or neither? ...
- math30 - Sequences 1)A sequence has a first term of 24 and every other term is ...
- Maths - An arithmetic and a geometric sequence have the same first terms.(2).......