document.write( "Question 1170387: Find all the natural numbers, which when divided by 7, leave the same number for the quotient and the remainder. \n" ); document.write( "

Algebra.Com's Answer #795269 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Let  \"n\"  be a natural number the problem asks for.\r\n" );
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document.write( "Then according to the condition, we can write\r\n" );
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document.write( "    n = 7*m + m\r\n" );
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document.write( "where an integer number  \"m\"  is the quotient and the remainder, at the same time.\r\n" );
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document.write( "As a remainder, the number  \"m\"  is under  inequalities  0 <= m <= 6;  so \"m\" may have these and only these values\r\n" );
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document.write( "     m = 0, 1, 2, 3, 4, 5, 6.\r\n" );
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document.write( "Accordingly, the number \"n\" may have these and only these values\r\n" );
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document.write( "    n = 7*0 + 0 = 0\r\n" );
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document.write( "    n = 7*1 + 1 = 8\r\n" );
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document.write( "    n = 7*2 + 2 = 16\r\n" );
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document.write( "    n = 7*3 + 3 = 24\r\n" );
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document.write( "    n = 7*4 + 4 = 32\r\n" );
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document.write( "    n = 7*5 + 5 = 40\r\n" );
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document.write( "    n = 7*6 + 6 = 48\r\n" );
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document.write( "ANSWER.  The possible values are  0, 8, 16, 24, 32, 40, 48.\r\n" );
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