Question #d0593

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Answer 1 · 2017-10-27T13:44:34

The answer is #344=7xx49+1=9xx38+2=11xx31+3#

We must this by try and error

let's look for #7a+1=9b+2#

#7xx0+1=1=9xx0+1#
#7xx1+1=8=9xx0+8#
#7xx2+1=15=9xx1+6#
#7xx3+1=22=9xx2+4#
#7xx4+1=29=9xx3+2-># solution

We can determine that solutions will repeat in a cycle of 63 so we can do like this:

#63+29=92=11xx8+4#
#92+63=155=14xx8+1#
#155+63=218=>11xx19+9#
#218+63=281=11xx25+6#
#281+63=344=9xx38+2->11xx31+3-># solution

in fact

#344=7xx49+1=9xx38+2=11xx31+3#

Other solution can be found by adding #(7xx9xx11)n#

#344+693=1037#
#1037+693=1730#

#etc.#

#693n+344#