A hint or full answer will help a lot, because I have no idea what to do.
Proof that $2^{10}+5^{12}$ is a composite number
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proof-explanation
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0http://www.wolframalpha.com/input/?i=factorize+2%5E10%2B5%5E12 – 2017-01-29
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2It is a number of the form $a^4+4b^4$ and $$ a^4+4b^4 = (a^2-2ab+2b^2)(a^2+2ab+2b^2)$$ – 2017-01-29
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0this has found Sophie Germain – 2017-01-29
2 Answers
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$$5^{12}+4\cdot 2^{8} = (5^6-2\cdot 5^3 \cdot 2^2+2\cdot 2^4)(5^6+2\cdot 5^3 \cdot 2^2+2\cdot 2^4)$$
Using $a^4+4b^4 =(a^2-2ab+2b^2)(a^2+2ab+2b^2)$
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Hint: This can be expressed as the difference of two squares in a reasonably easy way.
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1Note that factorising by using the difference of two squares is a respectable technique. – 2017-01-29