- let p and k prims,p>=2 and k>=2, - let a and b natural numbers ,a>=1 and b>=1, prove that for every n>=2 exist one a=(p-1)/2 and b=(k-1)/2 such that this equation n=a+b+1 is true . -for example : 2=(2-1)/2 +(2-1)/2 +1 2= 1/2 +1/2 +1 2=1+1 2=2 or 3=(3-1)/2 +(3-1)/2 +1 3=1+1+1 3=3 or 4=(5-1)/2 +(3-1)/2 +1 4=2+1+1 4=4

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- let p and k prims,p>=2 and k>=2, - let a and b natural numbers ,a>=1 and b>=1, prove that for every n>=2 exist one a=(p-1)/2 and b=(k-1)/2 such that this equation n=a+b+1 is true . -for example : 2=(2-1)/2 +(2-1)/2 +1 2= 1/2 +1/2 +1 2=1+1 2=2 or 3=(3-1)/2 +(3-1)/2 +1 3=1+1+1 3=3 or 4=(5-1)/2 +(3-1)/2 +1 4=2+1+1 4=4

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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n = (p-1)/2 + (k-1)/2 +1 = (p+k)/2. Thus, what the question is actually asking is to prove that are always an infinite number of primes>2 such that the sum of any two of them is even.But this is obviously true as any prime>2 is odd and the sum of two odd numbers is always even.

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