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Olympiad workbook
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IOQM
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Basics of Mathematics

Olympiad workbook · IOQM · Basics of Mathematics

Let a b c be a three digit number with nonzero digits such that...

Let abc‾\overline{a b c} be a three digit number with nonzero digits such that a2+b2=c2\mathrm{a}^2+\mathrm{b}^2=\mathrm{c}^2. What is the largest possible prime factor of abc‾\overline{a b c} ?

Correct answer

29

Step-by-step solution

a,b,c form Pythagoras triplet ⇒abc=345 or 435345=3×5×23 and 435=5×3×29\begin{aligned} & \Rightarrow \mathrm{abc}=345 \text { or } 435 \\ & 345=3 \times 5 \times 23 \text { and } 435=5 \times 3 \times 29 \end{aligned} ⇒\Rightarrow Largest possible prime factor =29=29
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