A class transposition is a permutation involution of the integers that exchanges two disjoint residue
classes term by term and fixes all other integers
(Kohl 2010). For 
,
,
and 
,
write 
and 
.
Their disjointness is equivalent to 
, where 
is the greatest common
divisor. The class transposition 
interchanges 
and 
for every integer 
. For example, 
swaps every even
number with the following odd number.
Iskra (2026) proved that if a product of two class transpositions has finite order, then its order
divides 840. The bound is sharp. The product of 
and 
has order 840,
which Kohl independently verified using GAP's RCWA package (Iskra 2026).
Iskra (2026) reports using ChatGPT to check arguments and search computationally for the order-840 example. The author states that all mathematical arguments and examples were independently verified.
