Giải
Ta có : abcd chia hết cho 29
=>(1000a+100b+10c+d)
=>(1000a+100b+10c+d) chia hết cho 29
=>2000a+200b+20c+2d
=>2000a+200b+20c+2d chia hết cho 29
=>(2001a+203b+29c+29d)−(a+3b+9c+27d)
=>(2001a+203b+29c+29d)−(a+3b+9c+27d) chia hết cho 29.
=>(29⋅69a+29⋅7b+29c+29d)−(a+3b+9c+27d)
=>(29⋅69a+29⋅7b+29c+29d)−(a+3b+9c+27d) chia hết cho 29
=>29⋅(69a+7b+c+d)−(a+3b+9c+27d)
=>29⋅(69a+7b+c+d)−(a+3b+9c+27d) chia hết cho 29
Vì 29⋅(69a+7b+c+d)29⋅(69a+7b+c+d) chia hết cho 29 và 29.(69a+7b+c+d)−(a+3b+9c+27d)29.(69a+7b+c+d)−(a+3b+9c+27d) chia hết cho 29
=>a+3b+9c+27d=>a+3b+9c+27d chia hết cho 29