document.write( "Question 1019875: Determine the truth value of the following statement.
\n" ); document.write( "If n = 4k + 1 for a natural k, then there are an even natural number a and an odd natural number b
\n" ); document.write( "such that n = a^2+b^2
\n" ); document.write( "Write the converse of this statement and determine its truth value as well. \n" ); document.write( "

Algebra.Com's Answer #635943 by robertb(5830) $\"\"$ $\"About$

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The statement is not always true. Take for example k = 5. Then n = 4*5 + 1 = 21, but 21 is not the sum of squares of odd and even natural numbers. (Another is when k = 8.)\r
\n" ); document.write( "\n" ); document.write( "The converse goes this way:
\n" ); document.write( "For all even natural number a and odd natural number b such that n = a^2+b^2, then there is a natural number k such that n = 4k + 1. (And because a statement and its converse are equivalent, the converse is also not true.) \n" ); document.write( "

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