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Which of the following CANNOT be expressed as the sum of squares of tw [#permalink]
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Question Stats: Hide Show timer StatisticsWhich of the following CANNOT be expressed as the sum of squares of two integer?A 13B 17C 21D 29 E 34
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Re: Which of the following CANNOT be expressed as the sum of squares of tw [#permalink]
Bunuel wrote: Which of the following CANNOT be expressed as the sum of squares of two integer?A 13B 17C 21D 29 E 34 As we don't have that many options, we'll test them all.This is an Alternative approach.We only need to look at the squares up to 5^2 (as 6^2 = 36 is larger than our largest value).So there are a total of 5 choose 2 = 10 options.1 + 4 = 51 + 9 = 101 + 16 = 17 **1 + 25 = 264 + 9 = 13 **4 + 16 = 204 + 25 = 29 **9 + 16 = 259 + 25 = 34 **16 + 25 = 41(C) is our answer. _________________
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Re: Which of the following CANNOT be expressed as the sum of squares of tw [#permalink]
Bunuel wrote: Which of the following CANNOT be expressed as the sum of squares of two integer?A 13B 17C 21D 29 E 34 13=2^2+3^217=4^2+1^221=Cannot be expressed29=5^2+2^234=5^2+3^2C
VP Joined: 31 Oct 2013 Posts: 1311 Concentration: Accounting, Finance GPA: 3.68 WE:Analyst (Accounting)
Re: Which of the following CANNOT be expressed as the sum of squares of tw [#permalink]
Bunuel wrote: Which of the following CANNOT be expressed as the sum of squares of two integer?A 13B 17C 21D 29 E 34 A bit tricky question. Number testing is the way to get the answer.\(3^2\) + \(2^2\) = 13\(4^2\) + \(1^1\) = 17\(5^2\)+ \(2^2\) = 29\(5^2\) + \(3^2\) = 34Now , option C is left. That's our answer. Try different number less than 21. There is a reason. 21 = 3*7 or 21*1. See none of the factors are square of an integer except 1. Thus it is also impossible to express 21 as a sum of the square of the 2 integers.The best answer is C.
Director Joined: 01 Oct 2017 Status:Learning stage Posts: 854 WE:Supply Chain Management (Energy and Utilities)
Re: Which of the following CANNOT be expressed as the sum of squares of tw [#permalink]
Bunuel wrote: Which of the following CANNOT be expressed as the sum of squares of two integer?A 13B 17C 21D 29 E 34 Every prime of the form (4k+1) can be expressed as the sum of two squares.. when the number is not prime:- If each of the factors of the integer can be written as the sum of two squares is itself expressible as the sum of two squares. Prime factorization of 34=2*17, (\(2=1^2+1^2\) & 17 is in the form of 4k+1. So, both 2 & 17 are perfect squares)Therefore, 34 is a sum of squares of two integer.So, eliminate E.Ans. (C) _________________
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Re: Which of the following CANNOT be expressed as the sum of squares of tw [#permalink] 12 Jul 2018, 12:59
A postive integer $n$ is representable as the sum of two squares, $n=x^2+y^2$ if and only if every prime divisor $p\equiv 3$ mod $4$ of $n$ occurs with even exponent. This is good enough to solve your questions. a) $n=363=3\cdot 11^2$ is not the sum of two squares, since $3$ is a prime divisor $p\equiv 3$ mod $4$ occuring not with even multiplicity. b) $n=700=2^2\cdot 5^2\cdot 7$ is not the sum of two squares. Take $p=7$. c) $n=34300=2^2\cdot 5^2\cdot 7^3$ is not the sum of two squares. Take $p=7$. d) $n=325=5^2\cdot 13$ is a sum of two squares, because every prime divisor $p\equiv 3$ mod $4$ occurs with even multiplicity - because $0$ is even. Of course, it is straightforward to see that, say, $325=10^2+15^2$. |
Which of the following can be expressed as sum of two squares
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