document.write( "Question 57847: Which of the following is a Pythagorean triple?
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\n" ); document.write( " a.6, 8, 12 b. 3, 4, 5 c. 1, 2, 3 d. 5, 7, 12\r
\n" ); document.write( "\n" ); document.write( "Which of the following remains an unsolved problem in mathematics?\r
\n" ); document.write( "\n" ); document.write( " a. Konigsberg Bridge Problem b. Fermat’s Last Theorem
\n" ); document.write( " c. Goldbach’s Conjecture D. Fundamental Theorem of Arithmetic\r
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\n" ); document.write( " a. 1 1 b. 1 4 6 4 1
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Algebra.Com's Answer #39533 by Edwin McCravy(20056)\"\" \"About 
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Which of the following is a Pythagorean triple?\r\n" );
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document.write( "a.   6, 8, 12 \r\n" );
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document.write( "     6² + 8² = \r\n" );
document.write( "     36 + 64 = \r\n" );
document.write( "         100\r\n" );
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document.write( "         12² = \r\n" );
document.write( "         144\r\n" );
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document.write( "100 does not equal 144, so this \r\n" );
document.write( "is not a Pythagorean triple.\r\n" );
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document.write( "b. 3, 4, 5 \r\n" );
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document.write( "     3² + 4² = \r\n" );
document.write( "      9 + 16 = \r\n" );
document.write( "          25\r\n" );
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document.write( "          5² = \r\n" );
document.write( "          25\r\n" );
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document.write( "These are both 25 and are both equal,\r\n" );
document.write( "so this IS a Pythagorean triple.\r\n" );
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document.write( "c. 1, 2, 3 \r\n" );
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document.write( "     1² + 2² = \r\n" );
document.write( "      1 +  4 = \r\n" );
document.write( "           5\r\n" );
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document.write( "          3² = \r\n" );
document.write( "           9\r\n" );
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document.write( "5 does not equal 9, so this is not a \r\n" );
document.write( "Pythagorean triple.\r\n" );
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document.write( "d. 5, 7, 12 \r\n" );
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document.write( "     5² + 7² = \r\n" );
document.write( "     25 + 49 = \r\n" );
document.write( "          74         \r\n" );
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document.write( "         12² = \r\n" );
document.write( "         144\r\n" );
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document.write( "74 does not equal 144, so this is not a Pythagorean triple.\r\n" );
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document.write( "So the answer is b\r\n" );
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document.write( "Which of the following remains an unsolved problem in mathematics? \r\n" );
document.write( "a. Konigsberg Bridge Problem\r\n" );
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document.write( "No for it can be proved that this can be done if there are\r\n" );
document.write( "an even number of bridges to cross and not if there are an\r\n" );
document.write( "odd number of bridges.\r\n" );
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document.write( " b. Fermat’s Last Theorem\r\n" );
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document.write( "Yes, this was solved by Wiles in the 90's. It states that if\r\n" );
document.write( "4 positive integers exist a, b, c, n so that an + bn = cn, \r\n" );
document.write( "then n must either be 1 or 2.\r\n" );
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document.write( "c. Goldbach’s Conjecture\r\n" );
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document.write( "No, this states that every even positive \r\n" );
document.write( "integer greater than 2 is the sum of two\r\n" );
document.write( "prime numbers. It has not been solved.\r\n" );
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document.write( "D. Fundamental Theorem of Arithmetic\r\n" );
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document.write( "This is that every positive integer has\r\n" );
document.write( "one and only one prime factorization.\r\n" );
document.write( "It has been proved.\r\n" );
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document.write( "So the answer is c. \r\n" );
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document.write( "Which is the third row of Pascal’s triangle?\r\n" );
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document.write( "Pascal's triangle is\r\n" );
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document.write( "             1            < -  first row\r\n" );
document.write( "           1   1          < -  second row\r\n" );
document.write( "         1   2   1        < -  third row\r\n" );
document.write( "       1   3   3   1      < -  fourth row\r\n" );
document.write( "     1   4   6   4   1    < -  fifth row\r\n" );
document.write( "   1   5  10  10   5   1  < -  sixth row\r\n" );
document.write( " ·   ·   ·   ·   ·   ·   ·\r\n" );
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document.write( "The third row is  1  2  1  \r\n" );
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document.write( "a. 1 1 b. 1 4 6 4 1\r\n" );
document.write( "c. 1 2 1 d. 1 3 3 1 \r\n" );
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document.write( "So the answer is c.\r\n" );
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document.write( "However, some authorities do not count the\r\n" );
document.write( "top row consisting of only the number 1.  \r\n" );
document.write( "If your teacher is one of these, then the \r\n" );
document.write( "answer is 1 3 3 1, or d.\r\n" );
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document.write( "Edwin

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