Be careful, that isn't the way that tower of exponents work. \( 3^ { 4 ^ 2 } = 3 ^ {16 } = \left( 3^4 \right) ^ 4 \). However, the series of modular arithmetic statements that you wrote are still true.

Note that you are supposed to show that they are the product of 2 digits with > 2015 digits. You have shown that it is a multiple of 5, but that is not sufficient to show that \(a, b\) exist.

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TopNewestHint :- \(x^4 + 4y^4 = (x^2 + 2y^2 - 2xy)(x^2 + 2y^2 + 2xy) \)

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Sophie Germain to the rescue!

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Be careful, that isn't the way that tower of exponents work. \( 3^ { 4 ^ 2 } = 3 ^ {16 } = \left( 3^4 \right) ^ 4 \). However, the series of modular arithmetic statements that you wrote are still true.

Note that you are supposed to show that they are the product of 2 digits with > 2015 digits. You have shown that it is a multiple of 5, but that is not sufficient to show that \(a, b\) exist.

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I'm a newbie in Number Theory. Thanks.

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