Why so

Algebra Level 4

\[ \dfrac{\left( 2^4 + \frac14\right)\left( 4^4 + \frac14\right)\left( 6^4 + \frac14\right)\left( 8^4 + \frac14\right)\left( 10^4 + \frac14\right)\left( 12^4 + \frac14\right)}{\left( 1^4 + \frac14\right)\left( 3^4 + \frac14\right)\left( 5^4 + \frac14\right)\left( 7^4 + \frac14\right)\left( 9^4 + \frac14\right)\left( 11^4 + \frac14\right)} \]

Prove that the number above is an integer, and find the number by simplification without actual calculation.

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