lambdaway :: babbage

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_h1 Charles Babbage

_ul [[http://rosettacode.org/wiki/Babbage_problem| http://rosettacode.org/wiki/Babbage_problem]]

_p What is the smallest positive integer whose square ends in the digits 269,696? Babbage thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain. This is a brute force but simple approach to get the two first ones:
{prewrap
'{S.map {lambda {:n} 
               {if {= {% {* :n :n} 1000000} 269696} 
                then :n{sup 2} = {* :n :n}  
                else}} 
       {S.serie {- {round {sqrt 269696}} 1} 100000 2}} 
-> {S.map {lambda {:n} {if {= {% {* :n :n} 1000000} 269696} then :n{sup 2} = {* :n :n} else}} 
          {S.serie {- {round {sqrt 269696}} 1} 100000 2}}

{round {sqrt 269696}}

25264^2 -> 638269696
99736^2 -> 9947269696
150264^2 -> 22579269696
224736^2 -> 50506269696
275264^2 -> 75770269696
349736^2 -> 122315269696
400264^2 -> 160211269696
474736^2 -> 225374269696
525264^2 -> 275902269696
599736^2 -> 359683269696 
}

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