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Yes I did it in Excel and filtered out the invalid values, then deleted them.
I had come to the point where the only acceptable value of k=6 but could not find a after this! That's because a turned out to be a huge number!
You did a great job!
Hi chen.aavaz,
I am glad that it fits well.
I found it by actual division of (10^n+k)/(k+1)^2
since k has to be low to meet demands of n I chose least possible value of k=6. denom=49
We do not know n.we know that with last remainder of 10000..../49 ,6 is to be appended to give a multiple of 49 . clearly it is 196.So we should look out for remainder 19. In my casio fx-825X calculator there is a button a b/c for integer division which gives dividend and remainder. Start with 100/49 = gives 2\frac {2}{49} remainder is not 19. To continue store it in memory and multiply by 10 ,look at remainder ,replace the number in memory by this number and go on multiplying by 10 until it gives decimal number.this is due to the ceiling on such operation.now recall the number in memory, write down integer part of division on paper (20408 in my calculation) and restart with remainder 8 and 0 to the right i.e 80 divide by 49 the same way from this batch I get integer as 1632 which you write on the right hand side of previous part(20408) and remainder 32 . continue the process until you get remainder of 19. Append 6 to the right and the dividend is 196/49=4 which is the last digit of number "a". i had done this much of work and posted it. I did not even calculate "b".I left it to chen.aavaz. He must have had horrible time for (a+b)^2.If you find calculator too tiresome you can try excel.
start with a series 100. 1000.10000,100000 on a column "a"say. in the next column use=quotient(a1,49) and in column c =mod(a1,49). Copy the formula to lower cells. however after a few cells down the calculation fails. Note down the last quotient and erase all failed values. and start with new series say 80,800,8000 etc (if 8 was the last remainder) continue the process until you spot remainder=19.
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Yesterday i just suggested calculation on excel sheet. today i actually tried it.
Last edited by thickhead (2016-05-14 21:08:16)
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I verified the answer as well and like chen.aavaz only missed it because of the size of a. n = 36. Well done (:
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