document.write( "Question 367082: A list of numbers 2, 4, 8, . . . is formed by doubling each of the preceding numbers. What is the remainder when the 15th number is divided by 6?\r
\n" ); document.write( "\n" ); document.write( "(A) 0 (B) 2 (C) 4 (D) 6 (E) 8 \n" ); document.write( "
Algebra.Com's Answer #261727 by Jk22(389)\"\" \"About 
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The number is 2^15
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\n" ); document.write( "the remainder of division by 6 can be 0,1,2,3,4,5, 0 is impossible since it's not divisible by 6
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\n" ); document.write( "1+6n is odd, hence cannot be 1 (except for 2^0=1)
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\n" ); document.write( "2+6n 2, is possible
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\n" ); document.write( "3 and 5 impossible since odd.\r
\n" ); document.write( "\n" ); document.write( "Hence the possible remainder are 2 or 4.
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\n" ); document.write( "Induction : let n>0
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\n" ); document.write( "Suppose 2^n has a remainder 2 divided by 6 : 2^n = 2 + 6n
\n" ); document.write( "then 2^(n+1)= 4 + 12n = 4 + 6*2n, the remainder were 4.
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\n" ); document.write( "Hence the remainder are alternating 2,4,2,\r
\n" ); document.write( "\n" ); document.write( "if the exponent is odd, the remainder is 2, else 4
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\n" ); document.write( "hence for 15, the remainder is 2, answer (B)
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