What is the smallest positive integer n such that 31 divides 5^n+n

[fossil crane]

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[clear berry]

what have you tried

also surely just like go through all the options at this point

[pastel meteor]

i tried to solve it with the options but any of them did not work, n=0, 31\1 , n=1, 6\31 , n=2, 25+2= 27, 27/31, n=3, 125+3=128\31(31 can divides 123 but not 128) , n=4 625+4=629/31 (31 can divides 620 not 629 ) so, maybe the options in this test are wrong or i just did not understand the question

[clear berry]

options might be wrong tbh

[buoyant garden]

Yes they are wrong

1/31 is not an integer 6/31 is not an integer 27/31 is not an integer 128/31 is not an integer 629/31 is not an integer

[austere anvil]

@pastel meteor

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