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-4 bytes thanks to Leaky Nun.
f=lambda n,x=1:(n+x)%(x+1)<1and~-n%-~x and x or f(n,x+1)or x
Try it online!Try it online!
f=lambda n,x=1:(n+x)%(x+1)<1and f(n,x+1)or x
Try it online!
f=lambda n,x=1:~-n%-~x and x or f(n,x+1)
