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anemone
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Positive integers $a$ and $b$ are such that $\dfrac{5a^4+a^2}{b^4+3b^2+4}$ is an integer. Prove that $a$ is composite.
A composite number is a positive integer that can be divided evenly by at least one number other than 1 and itself.
To prove that a number is composite, you can show that it is divisible by at least one number other than 1 and itself. This can be done through a variety of methods, such as using prime factorization or performing a division test.
No, a prime number is a positive integer that can only be divided evenly by 1 and itself. Therefore, it cannot be a composite number.
Proving that a number is composite can help in identifying its factors and understanding its properties. It can also be useful in determining the primality of a number and in various mathematical calculations.
Yes, every composite number can be expressed as a unique product of prime numbers. This is known as the fundamental theorem of arithmetic.