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anemone
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Let $a,\,b,\,c,\,d,\,e,\,f$ be positive integers and $S=a+b+c+d+e+f$. Suppose that the number $S$ divides $abc+def$ and $ab+bc+ca-de-ef-df$, prove that $S$ is composite.
A composite number is a positive integer that can be divided evenly by at least one number other than 1 and itself. In other words, it has more than two factors.
To prove that the sum of 6 positive integers is a composite number, we can show that it is divisible by at least one number other than 1 and itself. This can be done by finding the prime factorization of the sum and showing that it has more than two factors.
No, the sum of 6 positive integers cannot be a prime number because it is always divisible by at least 3, which means it has more than two factors and is therefore a composite number.
The smallest possible sum of 6 positive integers that is a composite number is 4, which can be shown by adding 1 + 1 + 1 + 1 + 1 + 1. This sum is divisible by 2 and 4, making it a composite number.
No, the sum of 6 positive integers cannot be an even prime number because all even numbers are divisible by 2, meaning they have more than two factors and are therefore composite numbers.