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Question Number 136830 by bramlexs22 last updated on 26/Mar/21
Determine all solutions in the integers of the following Diophantine equations: (a)56x+72y=40 (b)24x+138y=18 (c)221x+35y=11\n
Answered by floor(10²Eta[1]) last updated on 26/Mar/21
Extra close brace or missing open braceExtra close brace or missing open brace ⇒7x+9y=5 7x+9y=5(lookmod3) x≡2(mod3)⇒x=3a+2 7(3k+2)+9y=5 y=−1−73a⇒3∣a⇒a=3k x=9k+2,y=−1−7k Extra close brace or missing open braceExtra close brace or missing open brace ⇒4x+23y=3(lookmod2) y≡1(mod2)⇒y=2a+1 4x+23(2a+1)=3 x=−5−232a⇒2∣a⇒a=2k x=−5−23k,y=4k+1 Extra close brace or missing open braceExtra close brace or missing open brace x≡1(mod5)⇒x=5a+1 221(5a+1)+35y=11 y=−2217a−6⇒7∣a⇒a=7k x=35k+1,y=−221k−6
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