bloodhound Posted May 18, 2004 Share Posted May 18, 2004 Take a four digit positive number A, reverse the digits to make number B show that A^2 - B^2 is always divisible by 99 example: A=3785 B=5873 first question in my analysis exam today , dont know why. Link to comment Share on other sites More sharing options...
alext87 Posted May 18, 2004 Share Posted May 18, 2004 Does not work. Take A=1001 then B=1001 therefore Ans= 0 which is not divisble by 99. Link to comment Share on other sites More sharing options...
blike Posted May 18, 2004 Share Posted May 18, 2004 0/99 = 0 Link to comment Share on other sites More sharing options...
Dave Posted May 18, 2004 Share Posted May 18, 2004 Write a = 10^3*x1 + 10^2*x2 + 10*x3 + x4 and b similarly, expand the expression and show the coefficients are all factors of 99 is the first method that comes to mind. Link to comment Share on other sites More sharing options...
bloodhound Posted May 19, 2004 Author Share Posted May 19, 2004 dave, thats the first thing that came into my mind as well, but it takes hell of a job to expand A2-B2 the way i did it was to show that A-B is divisible by 9 and A+B is divisible by 11 i wonder if there are any better ways to work round it. i was about to use modular arithmetic but i am rubbish at that. Link to comment Share on other sites More sharing options...
Dave Posted May 19, 2004 Share Posted May 19, 2004 That's probably the best way. Link to comment Share on other sites More sharing options...
wolfson Posted May 19, 2004 Share Posted May 19, 2004 Try writing A in the form A=1000a+100b+10c+d, where a,b,c and d are the digits of A's decimal expansion. Then see what happens if you reverse and subtract. Ask if you need a further hint. Link to comment Share on other sites More sharing options...
Dave Posted May 19, 2004 Share Posted May 19, 2004 Try writing A in the form A=1000a+100b+10c+d' date='[/quote'] Write a = 10^3*x1 + 10^2*x2 + 10*x3 + x4 and b similarly, expand the expression and show the coefficients are all factors of 99 is the first method that comes to mind. Link to comment Share on other sites More sharing options...
wolfson Posted May 19, 2004 Share Posted May 19, 2004 Opps didnt see it i appologise. Should'nt just read question. lol Link to comment Share on other sites More sharing options...
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