### The Aureus Coffers

Saturday, October 29th, 2016The famous explorer Arbuthnot Smythe and his assistant Pascal stood before the stone door of an inaccessible ancient Roman underground tomb over which their torches showed was engraved “ET REQVIESCENT IBI TRES THESAURIS” in large letters.

Beside the door they saw three niches, each containing the bust of a lovely female aged from young to mature.

“Such exquisite sculpture work,” said Pascal full of admiration. “I wonder who the women were.”

“They appear to be related,” commented Arbuthnot, on an impulse pushing on the brooch sculpted on the older woman’s bust with his thumb and pulling her head forwards. This caused the stone door to open slowly on creaky hinges.

“Clever intuitive move,” exclaimed Pascal as they both entered and to their surprise saw that the interior of the tomb was illuminated by seven flaming lamps fixed around the walls.

They saw three exquisitely ornamented rectangular pools in each of which floated a perfectly preserved female body in serene repose, immersed in a transparent liquid. The older woman’s pool was placed on the left.

Arbuthnot Smythe and his assistant Pascal were speechless, eyes popping out and mouth dropping in wonder at this impossible spectacle.

After standing there for a while in a daze, Arbuthnot recovered himself sufficiently to speak. “I have read about this type of tomb in Blavatsky’s Isis book. It was for Cicero’s daughter,” he said in wonder. “Blavatsky even gives the formula for making these eternal flames. The tomb was found in the 19^{th} century, news of which was inevitably suppressed by religious authorities,” he related.

“What shall we do,” asked an astounded Pascal.

“Nothing,“ replied Arbuthnot sadly. “What we see here has been accomplished with knowledge of advanced spiritual technology. Science and western religions are not ready for this, least of all so-called modern medicine.”

“We will make a record of what we find for some future generation, when religion has evolved to become scientific and science to become religious,” he said quietly.

They switched their attention to the foot of each stone tomb, where they saw a marble coffer with the inscriptions “SUMMAM FACIAT QUADRATUM – DIFFERENTIA EST AEQUALIS.”

Arbuthnot forced open the first marble coffer with his sturdy knife. As the lid fell back, they saw that the coffer was full of gold coins.

Arbuthnot picked up a gold coin and studied it with a magnifying glass. “This is an aureus coin of the type minted by Julius Caesar,” he shouted jubilantly. “It contains about eight grams of gold. What a treasure we have found, Pascal.”

“Really unbelievable. I wonder what’s in the other marble coffers,” said Pascal, unsheathing his knife to pry open the next marble coffer lid. Again they found it was full of aureus coins, although this marble coffer was smaller. The third, even smaller marble coffer revealed the same: full of aureus coins.

“I wonder how many aureus coins there are in these marble coffers,” said Pascal scratching his head. “Based on their size, each one contains a smaller number of coins.”

“Judging from the engraved Roman text, I would say that the sum of the number of coins in any two marble coffers, taken pairwise, adds up to a square.” replied Arbuthnot, replacing his knife in its scabbard.

“Brilliant, then the difference between the number of coins in one marble coffer and the next descending one must be the same, judging from the second inscription,” added Pascal with a big smile.

“Yes indeed, that must be so,” exclaimed Arbuthnot. “Then we only have to do the math to determine how many coins there are in each of the marble coffers.”

“Well, being a purist, you do the math, Arbuthnot. To avoid a headache, I will use a computer,” laughed Pascal. Arbuthnot had already pulled out a notebook and was writing down the details in equation form.

“Yes, I wonder who the women were,” said Arbuthnot Smythe. “My guess is they were the wife and daughters of a nobleman who met with a sudden unfortunate fate. So he left his treasure with them.”

*Can you help Arbuthnot Smythe and Pascal work out how many gold coins each marble coffer contained?*