I know that Gauss introduced the symbol that adds a third horizontal bar to
the equal sign of Legendre for congruence of two numbers at the beginning
of his 1801 Disquisitiones arithmeticae.
Does that mean that Adrien-Marie Legendre wrote
a = b (mod m)?
I don't have immediate access to Legendre's
The'orie des nombres.
Perhaps it is in the U S Naval Academy Library.
Morris Kline in
MATHEMATICAL THOUGHT
states on page 813:
Though the notion of congruence did not originate with Gauss-- it
appears in the work of Euler, Lagrange, and Legendre--
He does not say how Euler, Lagrange, and Legendre wrote their congruences.
Help & (whether it is celebrated or not in your country) Happy Thanksgiving:
Best wishes from Annapolis,
Sam Kutler