Answer:
We can factorize the given expression as follows:512*517*519*520 + 520= 520(512*517*519 + 1)Now, we need to show that 512*517*519 + 1 is composite. We can use the fact that a^3 + b^3 = (a + b)(a^2 - ab + b^2), which can be derived from the sum of cubes formula. Let a = 512*517 and b = 1, then we have:a^3 + b^3 = (a + b)(a^2 - ab + b^2)= (512*517 + 1)((512*517)^2 - (512*517) + 1)Notice that (512*517)^2 - (512*517) + 1 is also a multiple of 512*517 + 1, since it satisfies the conditions of the sum of cubes formula with a = 512*517 and b = -1. Therefore, we have:512
Explanation:
We can factorize the given expression as follows:512*517*519*520 + 520= 520(512*517*519 + 1)Now, we need to show that 512*517*519 + 1 is composite. We can use the fact that a^3 + b^3 = (a + b)(a^2 - ab + b^2), which can be derived from the sum of cubes formula.Let a = 512*517 and b = 1, then we have:a^3 + b^3 = (a + b)(a^2 - ab + b^2)= (512*517 + 1)((512*517)^2 - (512*517) + 1)Notice that (512*517)^2 - (512*517) + 1 is also a multiple of 512*517 + 1, since it satisfies the conditions of the sum of cubes formula with a = 512*517 and b = -1. Therefore, we have:512